queryMockPaper = (postData, callback) => {
	let res = {
		"code": 200,
		"data": [{
				"paperId": "127D3E1EE0CC4284E065000000000001",
				"paperName": "心理健康教育",
				"semester": "2024-2025-1",
				"courseCode": "2220012114",
				"courseName": "心理健康教育",
				"beginDate": "2024-04-22",
				"endDate": "2025-04-28",
				"examTimeLimit": 60,
				"questionCount": 150,
				"score": 100,
				"errorCount": 79
			},
			{
				"paperId": "127D3E1EE0CC4284E065000000000002",
				"paperName": "军事理论",
				"semester": "2024-2025-1",
				"courseCode": "180005",
				"courseName": "军事理论",
				"beginDate": "2024-04-01",
				"endDate": "2025-04-01",
				"examTimeLimit": 60,
				"questionCount": 150,
				"score": 100,
				"errorCount": 64
			}
		]
	}
	callback(res)
}

queryErrorQuestion = (post, callback) => {
	let res = {
		code: 200,
		data: [{
				"paperId": "1816662617877135360",
				"questionTypeId": "1",
				"examQuestionVo": [{
						"paperDetailId": "91375",
						"paperId": "1816662617877135360",
						"questionId": "57728",
						"questionName": "如当 $x\\in \\left( \\ a\\ ,\\ b \\right)$时,${f}'\\left( x \\right)>0$ ,${f}''\\left( x \\right)<0$,则曲线$y=f\\left( x \\right)$在区间$\\left( \\ a\\ ,\\ b \\right)$ 上（ ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A70B0223E065FCFCFE0281A1",
								"examQuestionId": "57728",
								"optionName": "单调减且凸",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549325A90223E065FCFCFE0281A1",
								"examQuestionId": "57728",
								"optionName": "单调减且凹",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549622E50223E065FCFCFE0281A1",
								"examQuestionId": "57728",
								"optionName": "单调增且凹",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A4470223E065FCFCFE0281A1",
								"examQuestionId": "57728",
								"optionName": "单调增且凸",
								"isTrue": "1",
								"isChoose": "0"
							}
						],
						"explanation": "一阶导数大于零，曲线单调递增，二阶导数小于零，曲线为凸",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ['单调减且凹']
					}, {
						"paperDetailId": "91376",
						"paperId": "1816662617877135360",
						"questionId": "57701",
						"questionName": "以下哪些未定式可以直接利用洛必达法则求极限（    ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A6DB0223E065FCFCFE0281A1",
								"examQuestionId": "57701",
								"optionName": "$0\\cdot \\infty $",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549325790223E065FCFCFE0281A1",
								"examQuestionId": "57701",
								"optionName": "$\\infty -\\infty $",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549622B50223E065FCFCFE0281A1",
								"examQuestionId": "57701",
								"optionName": "${{0}^{0}}$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A4170223E065FCFCFE0281A1",
								"examQuestionId": "57701",
								"optionName": "$\\frac{0}{0}$",
								"isTrue": "1",
								"isChoose": "0"
							}
						],
						"explanation": "利用洛必达法则求极限的前提条件是未定式必须满足$\\frac{0}{0}$或$\\frac{\\infty }{\\infty }$",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$0\\cdot \\infty $"]
					},
					{
						"paperDetailId": "91377",
						"paperId": "1816662617877135360",
						"questionId": "57667",
						"questionName": "若$f(x)=\\arctan \\text{ }x$ ,则${f}'(0)$=（）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A60D0223E065FCFCFE0281A1",
								"examQuestionId": "57667",
								"optionName": "$0$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549324AB0223E065FCFCFE0281A1",
								"examQuestionId": "57667",
								"optionName": "$\\frac{1}{2}$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549621E70223E065FCFCFE0281A1",
								"examQuestionId": "57667",
								"optionName": "$2$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365494A3490223E065FCFCFE0281A1",
								"examQuestionId": "57667",
								"optionName": "$1$",
								"isTrue": "1",
								"isChoose": "0"
							}
						],
						"explanation": "${f}'(0)$=$\\frac{1}{1+{{x}^{2}}}\\left| _{x=0} \\right.=1$ ，选C",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$2$"]
					},
					{
						"paperDetailId": "91378",
						"paperId": "1816662617877135360",
						"questionId": "57629",
						"questionName": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{2}^{n}}-1}{{{3}^{n}}+1}=$（  ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A45C0223E065FCFCFE0281A1",
								"examQuestionId": "57629",
								"optionName": "$\\frac{2}{3}$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549322FA0223E065FCFCFE0281A1",
								"examQuestionId": "57629",
								"optionName": "$\\frac{3}{2}$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549620360223E065FCFCFE0281A1",
								"examQuestionId": "57629",
								"optionName": "$\\infty $",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A1980223E065FCFCFE0281A1",
								"examQuestionId": "57629",
								"optionName": "$0$",
								"isTrue": "1",
								"isChoose": "0"
							}
						],
						"explanation": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{2}^{n}}-1}{{{3}^{n}}+1}=\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( \\frac{2}{3} \\right)}^{n}}-{{\\left( \\frac{1}{3} \\right)}^{n}}}{1+{{\\left( \\frac{1}{3} \\right)}^{n}}}=\\frac{0-0}{1+0}=0$，故选C",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$\\frac{2}{3}$"]
					},
					{
						"paperDetailId": "91379",
						"paperId": "1816662617877135360",
						"questionId": "57665",
						"questionName": "若$f(x)=\\arcsin \\text{ }x$ ,则${f}'(x)$=（）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A5BA0223E065FCFCFE0281A1",
								"examQuestionId": "57665",
								"optionName": "$\\frac{1}{\\sqrt{1+{{x}^{2}}}}$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549324580223E065FCFCFE0281A1",
								"examQuestionId": "57665",
								"optionName": "$\\frac{1}{\\sqrt{1-{{x}^{2}}}}$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549621940223E065FCFCFE0281A1",
								"examQuestionId": "57665",
								"optionName": "$\\frac{1}{1-{{x}^{2}}}$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A2F60223E065FCFCFE0281A1",
								"examQuestionId": "57665",
								"optionName": "$\\frac{1}{1+{{x}^{2}}}$",
								"isTrue": "0",
								"isChoose": "1"
							}
						],
						"explanation": "$f'(x)=\\frac{1}{\\sqrt{1-{{x}^{2}}}}$ ，选B",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$\\frac{1}{1+{{x}^{2}}}$"]
					},
					{
						"paperDetailId": "91380",
						"paperId": "1816662617877135360",
						"questionId": "57710",
						"questionName": "下列解法中正确的是（ ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A6DD0223E065FCFCFE0281A1",
								"examQuestionId": "57710",
								"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\sin }^{2}}x}{x}\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{2\\sin x}{1}=0$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365493257B0223E065FCFCFE0281A1",
								"examQuestionId": "57710",
								"optionName": "$\\underset{x\\to {{0}^{+}}}{\\mathop{\\text{lim}}}\\,\\sin x\\ln x=0\\cdot \\infty =0$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A4190223E065FCFCFE0281A1",
								"examQuestionId": "57710",
								"optionName": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{x-1}{{{x}^{2}}-3x+2}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{1}{2x-3}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{0}{2}=0$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549622B70223E065FCFCFE0281A1",
								"examQuestionId": "57710",
								"optionName": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{1+{{x}^{2}}}{x+{{x}^{2}}}=\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{2x}{1+2x}=1$",
								"isTrue": "1",
								"isChoose": "0"
							}
						],
						"explanation": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{1+{{x}^{2}}}{x+{{x}^{2}}}=\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{2x}{1+2x}=1$",
						"answerVersionId": "1823895035833643008",
						"userAnswer": [
							"$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{x-1}{{{x}^{2}}-3x+2}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{1}{2x-3}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{0}{2}=0$"
						]
					}
				]
			},
			{
				"paperId": "1816662617877135361",
				"questionTypeId": "2",
				"examQuestionVo": [{
						"paperDetailId": "91381",
						"paperId": "1816662617877135360",
						"questionId": "57737",
						"questionName": "曲线y =${{x}^{3}}$的凸区间是（ ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A70D0223E065FCFCFE0281A1",
								"examQuestionId": "57737",
								"optionName": "$(-\\infty ,+\\infty )$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549325AB0223E065FCFCFE0281A1",
								"examQuestionId": "57737",
								"optionName": "$(0,+\\infty )$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365494A4490223E065FCFCFE0281A1",
								"examQuestionId": "57737",
								"optionName": "$(-\\infty ,0)$",
								"isTrue": "1",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549622E70223E065FCFCFE0281A1",
								"examQuestionId": "57737",
								"optionName": "$(-1,1)$",
								"isTrue": "0",
								"isChoose": "0"
							}
						],
						"explanation": "${y}'=3{{x}^{2}},{y}''=6x,{y}''=0\\text{ } x=0$，当$x<0$时,${y}''<0$",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$(-\\infty ,0)$", "$(-\\infty ,0)$"]
					},
					{
						"paperDetailId": "91382",
						"paperId": "1816662617877135360",
						"questionId": "57639",
						"questionName": "当$x\\to 0$时，与$\\sqrt{1+x}-\\sqrt{1-x}$等价无穷小的是（  ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A6D00223E065FCFCFE0281A1",
								"examQuestionId": "57639",
								"optionName": "$x$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365493256E0223E065FCFCFE0281A1",
								"examQuestionId": "57639",
								"optionName": "$2x$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A40C0223E065FCFCFE0281A1",
								"examQuestionId": "57639",
								"optionName": "${{x}^{2}}$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549622AA0223E065FCFCFE0281A1",
								"examQuestionId": "57639",
								"optionName": "$2{{x}^{2}}$",
								"isTrue": "1",
								"isChoose": "0"
							}
						],
						"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sqrt{1+x}-\\sqrt{1-x}}{x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{(1+x)-(1-x)}{x(\\sqrt{1+x}+\\sqrt{1-x})}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{2}{\\sqrt{1+x}+\\sqrt{1-x}}=1$ ，故选A",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["${{x}^{2}}$"]
					},
					{
						"paperDetailId": "91383",
						"paperId": "1816662617877135360",
						"questionId": "57664",
						"questionName": "若$f(x)=\\tan \\text{ }x$,则${f}'(x)$= （）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A5B90223E065FCFCFE0281A1",
								"examQuestionId": "57664",
								"optionName": "${{\\sin }^{2}}x$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549324570223E065FCFCFE0281A1",
								"examQuestionId": "57664",
								"optionName": "${{\\cos }^{2}}x$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A2F50223E065FCFCFE0281A1",
								"examQuestionId": "57664",
								"optionName": "${{\\sec }^{2}}x$",
								"isTrue": "1",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549621930223E065FCFCFE0281A1",
								"examQuestionId": "57664",
								"optionName": "${{\\csc }^{2}}x$",
								"isTrue": "0",
								"isChoose": "1"
							}
						],
						"explanation": "${f}'(x)={{\\sec }^{2}}x$ ，选C",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["${{\\csc }^{2}}x$", "${{\\csc }^{2}}x$"]
					},
					{
						"paperDetailId": "91384",
						"paperId": "1816662617877135360",
						"questionId": "57718",
						"questionName": "函数 $f(x)=2{{x}^{3}}-6{{x}^{2}}-18x-7$的极小值是（ ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A43D0223E065FCFCFE0281A1",
								"examQuestionId": "57718",
								"optionName": "$f(-1)=3$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549322DB0223E065FCFCFE0281A1",
								"examQuestionId": "57718",
								"optionName": "$f(3)=-61$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549620170223E065FCFCFE0281A1",
								"examQuestionId": "57718",
								"optionName": "$f(0)=-7$",
								"isTrue": "1",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365494A1790223E065FCFCFE0281A1",
								"examQuestionId": "57718",
								"optionName": "$f(1)=-29$",
								"isTrue": "0",
								"isChoose": "1"
							}
						],
						"explanation": "${f}'(x)=6{{x}^{2}}-12x-18=6(x+1)(x-3)$，驻点${{x}_{1}}=-1,{{x}_{2}}=3,$$f(x)$在$\\left[ -1,3 \\right]$上单调减少，在$[3,+\\infty )$上单调增加",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$f(0)=-7$", "$f(1)=-29$"]
					},
					{
						"paperDetailId": "91385",
						"paperId": "1816662617877135360",
						"questionId": "57651",
						"questionName": "若$f(x)$在${{x}_{0}}$处可导，则${f}'({{x}_{0}})$=  （ ）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A6090223E065FCFCFE0281A1",
								"examQuestionId": "57651",
								"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}})-f({{x}_{0}}+\\Delta x)}{\\Delta x}$",
								"isTrue": "1",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549324A70223E065FCFCFE0281A1",
								"examQuestionId": "57651",
								"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}}-\\Delta x)-f({{x}_{0}})}{\\Delta x}$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365494A3450223E065FCFCFE0281A1",
								"examQuestionId": "57651",
								"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}}+\\Delta x)-f({{x}_{0}})}{\\Delta x}$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549621E30223E065FCFCFE0281A1",
								"examQuestionId": "57651",
								"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f(x+{{x}_{0}})+f({{x}_{0}})}{\\Delta x}$",
								"isTrue": "0",
								"isChoose": "0"
							}
						],
						"explanation": "由导数定义，${f}'({{x}_{0}})\\underset{\\Delta x\\to 0}{\\mathop{\\text{=lim}}}\\,\\frac{f({{x}_{0}}+\\Delta x)-f({{x}_{0}})}{\\Delta x}$",
						"answerVersionId": "1823895035833643008",
						"userAnswer": [
							"${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}})-f({{x}_{0}}+\\Delta x)}{\\Delta x}$",
							"${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}}-\\Delta x)-f({{x}_{0}})}{\\Delta x}$"
						]
					},
					{
						"paperDetailId": "91386",
						"paperId": "1816662617877135360",
						"questionId": "57663",
						"questionName": "若$f(x)={{e}^{x}}$,则${f}'(0)$= （）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A49C0223E065FCFCFE0281A1",
								"examQuestionId": "57663",
								"optionName": "0",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365493233A0223E065FCFCFE0281A1",
								"examQuestionId": "57663",
								"optionName": "1",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549620760223E065FCFCFE0281A1",
								"examQuestionId": "57663",
								"optionName": "e",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A1D80223E065FCFCFE0281A1",
								"examQuestionId": "57663",
								"optionName": "2",
								"isTrue": "0",
								"isChoose": "1"
							}
						],
						"explanation": "${f}'(0)={{e}^{x}}{{|}_{x=0}}=1$， 选B",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["0", "2"]
					},
					{
						"paperDetailId": "91387",
						"paperId": "1816662617877135360",
						"questionId": "57666",
						"questionName": "若$f(x)=\\arctan \\text{ }x$ ,则${f}'(x)$=（）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A5BB0223E065FCFCFE0281A1",
								"examQuestionId": "57666",
								"optionName": "$1+{{x}^{2}}$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "1036549324590223E065FCFCFE0281A1",
								"examQuestionId": "57666",
								"optionName": "$1-{{x}^{2}}$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365494A2F70223E065FCFCFE0281A1",
								"examQuestionId": "57666",
								"optionName": "$\\frac{1}{1+{{x}^{2}}}$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549621950223E065FCFCFE0281A1",
								"examQuestionId": "57666",
								"optionName": "$\\frac{1}{1-{{x}^{2}}}$",
								"isTrue": "1",
								"isChoose": "1"
							}
						],
						"explanation": "${f}'(x)=\\frac{1}{1+{{x}^{2}}}$ ，选C",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$1+{{x}^{2}}$", "$\\frac{1}{1-{{x}^{2}}}$"]
					},
					{
						"paperDetailId": "91388",
						"paperId": "1816662617877135360",
						"questionId": "57672",
						"questionName": "若$f(x)={{x}^{2}}{{e}^{x}}$,则${f}'(x)=$（）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A3BE0223E065FCFCFE0281A1",
								"examQuestionId": "57672",
								"optionName": "$\\text{2}x\\cdot {{e}^{x}}+{{x}^{2}}\\cdot {{e}^{x}}$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "10365493225C0223E065FCFCFE0281A1",
								"examQuestionId": "57672",
								"optionName": "$2x\\cdot {{e}^{x}}-{{x}^{2}}\\cdot {{e}^{x}}$",
								"isTrue": "0",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "103654961F980223E065FCFCFE0281A1",
								"examQuestionId": "57672",
								"optionName": "$2x-{{e}^{x}}$",
								"isTrue": "1",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365494A0FA0223E065FCFCFE0281A1",
								"examQuestionId": "57672",
								"optionName": "$\\text{2}x+{{e}^{x}}$",
								"isTrue": "0",
								"isChoose": "0"
							}
						],
						"explanation": "${f}'(x)$=$\\text{2}x\\cdot {{e}^{x}}+{{x}^{2}}\\cdot {{e}^{x}}$ ，选A",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$2x\\cdot {{e}^{x}}-{{x}^{2}}\\cdot {{e}^{x}}$",
							"$2x-{{e}^{x}}$"
						]
					},
					{
						"paperDetailId": "91389",
						"paperId": "1816662617877135360",
						"questionId": "57698",
						"questionName": "若$f(x)={{e}^{2x}}$,则$dy{{|}_{x=1}}=$（）",
						"questionScore": "1",
						"questionOptionList": [{
								"examQuestionOptionId": "10365491A5F30223E065FCFCFE0281A1",
								"examQuestionId": "57698",
								"optionName": "$2{{e}^{2}}dx$",
								"isTrue": "1",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549324910223E065FCFCFE0281A1",
								"examQuestionId": "57698",
								"optionName": "$2edx$",
								"isTrue": "1",
								"isChoose": "1"
							},
							{
								"examQuestionOptionId": "10365494A32F0223E065FCFCFE0281A1",
								"examQuestionId": "57698",
								"optionName": "${{e}^{2}}dx$",
								"isTrue": "0",
								"isChoose": "0"
							},
							{
								"examQuestionOptionId": "1036549621CD0223E065FCFCFE0281A1",
								"examQuestionId": "57698",
								"optionName": "$edx$",
								"isTrue": "0",
								"isChoose": "1"
							}
						],
						"explanation": "$dy{{|}_{x=1}}={f}'(x)dx{{|}_{x=1}}=2{{e}^{2}}dx$ 选A",
						"answerVersionId": "1823895035833643008",
						"userAnswer": ["$2edx$", "$edx$"]
					}
				]
			}
		]
	};
	callback(res)
}

queryMockQuestion = (postData, callback) => {
	let res = {
		"code": 200,
		"data": [{
			"paperId": "1816662617877135360",
			"questionTypeId": "1",
			"examQuestionVo": [{
					"paperDetailId": "91375",
					"paperId": "1816662617877135360",
					"questionId": "57728",
					"questionName": "如当 $x\\in \\left( \\ a\\ ,\\ b \\right)$时,${f}'\\left( x \\right)>0$ ,${f}''\\left( x \\right)<0$,则曲线$y=f\\left( x \\right)$在区间$\\left( \\ a\\ ,\\ b \\right)$ 上（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A70B0223E065FCFCFE0281A1",
							"examQuestionId": "57728",
							"optionName": "单调减且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A90223E065FCFCFE0281A1",
							"examQuestionId": "57728",
							"optionName": "单调减且凹",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E50223E065FCFCFE0281A1",
							"examQuestionId": "57728",
							"optionName": "单调增且凹",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4470223E065FCFCFE0281A1",
							"examQuestionId": "57728",
							"optionName": "单调增且凸",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "一阶导数大于零，曲线单调递增，二阶导数小于零，曲线为凸",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91376",
					"paperId": "1816662617877135360",
					"questionId": "57701",
					"questionName": "以下哪些未定式可以直接利用洛必达法则求极限（    ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6DB0223E065FCFCFE0281A1",
							"examQuestionId": "57701",
							"optionName": "$0\\cdot \\infty $",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325790223E065FCFCFE0281A1",
							"examQuestionId": "57701",
							"optionName": "$\\infty -\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B50223E065FCFCFE0281A1",
							"examQuestionId": "57701",
							"optionName": "${{0}^{0}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4170223E065FCFCFE0281A1",
							"examQuestionId": "57701",
							"optionName": "$\\frac{0}{0}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "利用洛必达法则求极限的前提条件是未定式必须满足$\\frac{0}{0}$或$\\frac{\\infty }{\\infty }$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91377",
					"paperId": "1816662617877135360",
					"questionId": "57667",
					"questionName": "若$f(x)=\\arctan \\text{ }x$ ,则${f}'(0)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A60D0223E065FCFCFE0281A1",
							"examQuestionId": "57667",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324AB0223E065FCFCFE0281A1",
							"examQuestionId": "57667",
							"optionName": "$\\frac{1}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621E70223E065FCFCFE0281A1",
							"examQuestionId": "57667",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3490223E065FCFCFE0281A1",
							"examQuestionId": "57667",
							"optionName": "$1$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(0)$=$\\frac{1}{1+{{x}^{2}}}\\left| _{x=0} \\right.=1$ ，选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91378",
					"paperId": "1816662617877135360",
					"questionId": "57629",
					"questionName": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{2}^{n}}-1}{{{3}^{n}}+1}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A45C0223E065FCFCFE0281A1",
							"examQuestionId": "57629",
							"optionName": "$\\frac{2}{3}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322FA0223E065FCFCFE0281A1",
							"examQuestionId": "57629",
							"optionName": "$\\frac{3}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620360223E065FCFCFE0281A1",
							"examQuestionId": "57629",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1980223E065FCFCFE0281A1",
							"examQuestionId": "57629",
							"optionName": "$0$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{2}^{n}}-1}{{{3}^{n}}+1}=\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( \\frac{2}{3} \\right)}^{n}}-{{\\left( \\frac{1}{3} \\right)}^{n}}}{1+{{\\left( \\frac{1}{3} \\right)}^{n}}}=\\frac{0-0}{1+0}=0$，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91379",
					"paperId": "1816662617877135360",
					"questionId": "57665",
					"questionName": "若$f(x)=\\arcsin \\text{ }x$ ,则${f}'(x)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5BA0223E065FCFCFE0281A1",
							"examQuestionId": "57665",
							"optionName": "$\\frac{1}{\\sqrt{1+{{x}^{2}}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324580223E065FCFCFE0281A1",
							"examQuestionId": "57665",
							"optionName": "$\\frac{1}{\\sqrt{1-{{x}^{2}}}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621940223E065FCFCFE0281A1",
							"examQuestionId": "57665",
							"optionName": "$\\frac{1}{1-{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2F60223E065FCFCFE0281A1",
							"examQuestionId": "57665",
							"optionName": "$\\frac{1}{1+{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$f'(x)=\\frac{1}{\\sqrt{1-{{x}^{2}}}}$ ，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91380",
					"paperId": "1816662617877135360",
					"questionId": "57710",
					"questionName": "下列解法中正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6DD0223E065FCFCFE0281A1",
							"examQuestionId": "57710",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\sin }^{2}}x}{x}\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{2\\sin x}{1}=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493257B0223E065FCFCFE0281A1",
							"examQuestionId": "57710",
							"optionName": "$\\underset{x\\to {{0}^{+}}}{\\mathop{\\text{lim}}}\\,\\sin x\\ln x=0\\cdot \\infty =0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4190223E065FCFCFE0281A1",
							"examQuestionId": "57710",
							"optionName": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{x-1}{{{x}^{2}}-3x+2}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{1}{2x-3}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{0}{2}=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B70223E065FCFCFE0281A1",
							"examQuestionId": "57710",
							"optionName": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{1+{{x}^{2}}}{x+{{x}^{2}}}=\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{2x}{1+2x}=1$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{1+{{x}^{2}}}{x+{{x}^{2}}}=\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{2x}{1+2x}=1$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91381",
					"paperId": "1816662617877135360",
					"questionId": "57737",
					"questionName": "曲线y =${{x}^{3}}$的凸区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A70D0223E065FCFCFE0281A1",
							"examQuestionId": "57737",
							"optionName": "$(-\\infty ,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325AB0223E065FCFCFE0281A1",
							"examQuestionId": "57737",
							"optionName": "$(0,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4490223E065FCFCFE0281A1",
							"examQuestionId": "57737",
							"optionName": "$(-\\infty ,0)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E70223E065FCFCFE0281A1",
							"examQuestionId": "57737",
							"optionName": "$(-1,1)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=3{{x}^{2}},{y}''=6x,{y}''=0\\text{ } x=0$，当$x<0$时,${y}''<0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91382",
					"paperId": "1816662617877135360",
					"questionId": "57639",
					"questionName": "当$x\\to 0$时，与$\\sqrt{1+x}-\\sqrt{1-x}$等价无穷小的是（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D00223E065FCFCFE0281A1",
							"examQuestionId": "57639",
							"optionName": "$x$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493256E0223E065FCFCFE0281A1",
							"examQuestionId": "57639",
							"optionName": "$2x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A40C0223E065FCFCFE0281A1",
							"examQuestionId": "57639",
							"optionName": "${{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622AA0223E065FCFCFE0281A1",
							"examQuestionId": "57639",
							"optionName": "$2{{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sqrt{1+x}-\\sqrt{1-x}}{x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{(1+x)-(1-x)}{x(\\sqrt{1+x}+\\sqrt{1-x})}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{2}{\\sqrt{1+x}+\\sqrt{1-x}}=1$ ，故选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91383",
					"paperId": "1816662617877135360",
					"questionId": "57664",
					"questionName": "若$f(x)=\\tan \\text{ }x$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5B90223E065FCFCFE0281A1",
							"examQuestionId": "57664",
							"optionName": "${{\\sin }^{2}}x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324570223E065FCFCFE0281A1",
							"examQuestionId": "57664",
							"optionName": "${{\\cos }^{2}}x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2F50223E065FCFCFE0281A1",
							"examQuestionId": "57664",
							"optionName": "${{\\sec }^{2}}x$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621930223E065FCFCFE0281A1",
							"examQuestionId": "57664",
							"optionName": "${{\\csc }^{2}}x$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)={{\\sec }^{2}}x$ ，选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91384",
					"paperId": "1816662617877135360",
					"questionId": "57718",
					"questionName": "函数 $f(x)=2{{x}^{3}}-6{{x}^{2}}-18x-7$的极小值是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A43D0223E065FCFCFE0281A1",
							"examQuestionId": "57718",
							"optionName": "$f(-1)=3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322DB0223E065FCFCFE0281A1",
							"examQuestionId": "57718",
							"optionName": "$f(3)=-61$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620170223E065FCFCFE0281A1",
							"examQuestionId": "57718",
							"optionName": "$f(0)=-7$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1790223E065FCFCFE0281A1",
							"examQuestionId": "57718",
							"optionName": "$f(1)=-29$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=6{{x}^{2}}-12x-18=6(x+1)(x-3)$，驻点${{x}_{1}}=-1,{{x}_{2}}=3,$$f(x)$在$\\left[ -1,3 \\right]$上单调减少，在$[3,+\\infty )$上单调增加",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91385",
					"paperId": "1816662617877135360",
					"questionId": "57651",
					"questionName": "若$f(x)$在${{x}_{0}}$处可导，则${f}'({{x}_{0}})$=  （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6090223E065FCFCFE0281A1",
							"examQuestionId": "57651",
							"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}})-f({{x}_{0}}+\\Delta x)}{\\Delta x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324A70223E065FCFCFE0281A1",
							"examQuestionId": "57651",
							"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}}-\\Delta x)-f({{x}_{0}})}{\\Delta x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3450223E065FCFCFE0281A1",
							"examQuestionId": "57651",
							"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f({{x}_{0}}+\\Delta x)-f({{x}_{0}})}{\\Delta x}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621E30223E065FCFCFE0281A1",
							"examQuestionId": "57651",
							"optionName": "${f}'({{x}_{0}})=\\underset{\\Delta x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{f(x+{{x}_{0}})+f({{x}_{0}})}{\\Delta x}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由导数定义，${f}'({{x}_{0}})\\underset{\\Delta x\\to 0}{\\mathop{\\text{=lim}}}\\,\\frac{f({{x}_{0}}+\\Delta x)-f({{x}_{0}})}{\\Delta x}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91386",
					"paperId": "1816662617877135360",
					"questionId": "57663",
					"questionName": "若$f(x)={{e}^{x}}$,则${f}'(0)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A49C0223E065FCFCFE0281A1",
							"examQuestionId": "57663",
							"optionName": "0",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493233A0223E065FCFCFE0281A1",
							"examQuestionId": "57663",
							"optionName": "1",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620760223E065FCFCFE0281A1",
							"examQuestionId": "57663",
							"optionName": "e",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1D80223E065FCFCFE0281A1",
							"examQuestionId": "57663",
							"optionName": "2",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(0)={{e}^{x}}{{|}_{x=0}}=1$， 选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91387",
					"paperId": "1816662617877135360",
					"questionId": "57666",
					"questionName": "若$f(x)=\\arctan \\text{ }x$ ,则${f}'(x)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5BB0223E065FCFCFE0281A1",
							"examQuestionId": "57666",
							"optionName": "$1+{{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324590223E065FCFCFE0281A1",
							"examQuestionId": "57666",
							"optionName": "$1-{{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2F70223E065FCFCFE0281A1",
							"examQuestionId": "57666",
							"optionName": "$\\frac{1}{1+{{x}^{2}}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621950223E065FCFCFE0281A1",
							"examQuestionId": "57666",
							"optionName": "$\\frac{1}{1-{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=\\frac{1}{1+{{x}^{2}}}$ ，选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91388",
					"paperId": "1816662617877135360",
					"questionId": "57672",
					"questionName": "若$f(x)={{x}^{2}}{{e}^{x}}$,则${f}'(x)=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3BE0223E065FCFCFE0281A1",
							"examQuestionId": "57672",
							"optionName": "$\\text{2}x\\cdot {{e}^{x}}+{{x}^{2}}\\cdot {{e}^{x}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493225C0223E065FCFCFE0281A1",
							"examQuestionId": "57672",
							"optionName": "$2x\\cdot {{e}^{x}}-{{x}^{2}}\\cdot {{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F980223E065FCFCFE0281A1",
							"examQuestionId": "57672",
							"optionName": "$2x-{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0FA0223E065FCFCFE0281A1",
							"examQuestionId": "57672",
							"optionName": "$\\text{2}x+{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=$\\text{2}x\\cdot {{e}^{x}}+{{x}^{2}}\\cdot {{e}^{x}}$ ，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91389",
					"paperId": "1816662617877135360",
					"questionId": "57698",
					"questionName": "若$f(x)={{e}^{2x}}$,则$dy{{|}_{x=1}}=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F30223E065FCFCFE0281A1",
							"examQuestionId": "57698",
							"optionName": "$2{{e}^{2}}dx$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324910223E065FCFCFE0281A1",
							"examQuestionId": "57698",
							"optionName": "$2edx$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A32F0223E065FCFCFE0281A1",
							"examQuestionId": "57698",
							"optionName": "${{e}^{2}}dx$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621CD0223E065FCFCFE0281A1",
							"examQuestionId": "57698",
							"optionName": "$edx$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$dy{{|}_{x=1}}={f}'(x)dx{{|}_{x=1}}=2{{e}^{2}}dx$ 选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91390",
					"paperId": "1816662617877135360",
					"questionId": "57714",
					"questionName": "函数$f(x)=2{{x}^{3}}-6{{x}^{2}}-18x-7$的驻点有（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F60223E065FCFCFE0281A1",
							"examQuestionId": "57714",
							"optionName": "$x=-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324940223E065FCFCFE0281A1",
							"examQuestionId": "57714",
							"optionName": "$x=3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3320223E065FCFCFE0281A1",
							"examQuestionId": "57714",
							"optionName": "${{x}_{1}}=-1,{{x}_{2}}=-3,$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621D00223E065FCFCFE0281A1",
							"examQuestionId": "57714",
							"optionName": "${{x}_{1}}=-1,{{x}_{2}}=3$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=6{{x}^{2}}-12x-18=6(x+1)(x-3)$，由${f}'(x)=0$得D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91391",
					"paperId": "1816662617877135360",
					"questionId": "57734",
					"questionName": "曲线y =${{x}^{2}}$－${{x}^{3}}$的凸区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4750223E065FCFCFE0281A1",
							"examQuestionId": "57734",
							"optionName": "$(-\\infty ,\\frac{1}{3})$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323130223E065FCFCFE0281A1",
							"examQuestionId": "57734",
							"optionName": "$(\\frac{1}{3},+\\infty )$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1B10223E065FCFCFE0281A1",
							"examQuestionId": "57734",
							"optionName": "$(-\\infty ,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496204F0223E065FCFCFE0281A1",
							"examQuestionId": "57734",
							"optionName": "无",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=2x-3{{x}^{2}},{y}''=2-6x,{y}''=0\\text{ } x=\\frac{1}{3}$，当$x>\\frac{1}{3}$时,${y}''<0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91392",
					"paperId": "1816662617877135360",
					"questionId": "57656",
					"questionName": "若$s={{t}^{3}}+2{{t}^{2}}-5\\ $,则物体在$t=2$时的加速度为（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3BA0223E065FCFCFE0281A1",
							"examQuestionId": "57656",
							"optionName": "8",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322580223E065FCFCFE0281A1",
							"examQuestionId": "57656",
							"optionName": "10",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0F60223E065FCFCFE0281A1",
							"examQuestionId": "57656",
							"optionName": "16",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F940223E065FCFCFE0281A1",
							"examQuestionId": "57656",
							"optionName": "14",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由$s'=3{{t}^{2}}+4t$，${{S}^{\\prime \\prime }}=6t+4,$ 所以$a={{S}^{\\prime \\prime }}{{|}_{t=2}}=16$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91393",
					"paperId": "1816662617877135360",
					"questionId": "57688",
					"questionName": "若$x\\cdot y-{{e}^{x}}+\\text{ }{{e}^{y}}=0$,则$\\frac{dy}{dx}=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3C10223E065FCFCFE0281A1",
							"examQuestionId": "57688",
							"optionName": "$\\frac{{{e}^{x}}-y}{x+{{e}^{y}}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493225F0223E065FCFCFE0281A1",
							"examQuestionId": "57688",
							"optionName": "$\\frac{{{e}^{x}}+y}{x+{{e}^{y}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0FD0223E065FCFCFE0281A1",
							"examQuestionId": "57688",
							"optionName": "$\\frac{{{e}^{x}}-y}{x-{{e}^{y}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F9B0223E065FCFCFE0281A1",
							"examQuestionId": "57688",
							"optionName": "$\\frac{{{e}^{x}}+y}{x-{{e}^{y}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\left( x\\cdot y-{{e}^{x}}+\\text{ }{{e}^{y}} \\right)&#39;=0$ ，$y&#39;=$$\\frac{{{e}^{x}}-y}{x+{{e}^{y}}}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91394",
					"paperId": "1816662617877135360",
					"questionId": "57708",
					"questionName": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{x}}}{x}=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3F80223E065FCFCFE0281A1",
							"examQuestionId": "57708",
							"optionName": "0",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322960223E065FCFCFE0281A1",
							"examQuestionId": "57708",
							"optionName": "1",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961FD20223E065FCFCFE0281A1",
							"examQuestionId": "57708",
							"optionName": "3",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1340223E065FCFCFE0281A1",
							"examQuestionId": "57708",
							"optionName": "$+\\infty $",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{x}}}{x}=$$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( {{\\text{e}}^{x}} \\right)}^{\\prime }}}{{{\\left( x \\right)}^{\\prime }}}=\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}}{1}=+\\infty $",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91395",
					"paperId": "1816662617877135360",
					"questionId": "57635",
					"questionName": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{n}){{}^{kn}}={{e}^{-3}}$,则$k=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5D10223E065FCFCFE0281A1",
							"examQuestionId": "57635",
							"optionName": "$\\frac{3}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493246F0223E065FCFCFE0281A1",
							"examQuestionId": "57635",
							"optionName": "$\\frac{2}{3}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A30D0223E065FCFCFE0281A1",
							"examQuestionId": "57635",
							"optionName": "$-\\frac{3}{2}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621AB0223E065FCFCFE0281A1",
							"examQuestionId": "57635",
							"optionName": "$-\\frac{2}{3}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\because \\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{n}){{}^{kn}}={{e}^{2k}}={{e}^{-3}},\\therefore k=-\\frac{3}{2}$，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91396",
					"paperId": "1816662617877135360",
					"questionId": "57638",
					"questionName": "当$x\\to 0$时,与无穷小$x+100{{x}^{3}}$等价无穷小的是 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6CF0223E065FCFCFE0281A1",
							"examQuestionId": "57638",
							"optionName": "$\\sqrt[3]{x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493256D0223E065FCFCFE0281A1",
							"examQuestionId": "57638",
							"optionName": "$\\sqrt{x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A40B0223E065FCFCFE0281A1",
							"examQuestionId": "57638",
							"optionName": "$x$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622A90223E065FCFCFE0281A1",
							"examQuestionId": "57638",
							"optionName": "$100{{x}^{3}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x+100{{x}^{3}}}{x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{1+100{{x}^{2}}}{1}=\\frac{1+0}{1}=1$ ，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91397",
					"paperId": "1816662617877135360",
					"questionId": "57644",
					"questionName": "函数$f\\left( x \\right)=\\left\\{ \\begin{matrix}   2x,\\ \\quad 0\\le x<1  \\\\   2-x,1\\le x\\le 2  \\\\\\end{matrix} \\right.$的连续区间是（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5D40223E065FCFCFE0281A1",
							"examQuestionId": "57644",
							"optionName": "$\\left[ 0,2 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324720223E065FCFCFE0281A1",
							"examQuestionId": "57644",
							"optionName": "$\\left[ 0,1 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3100223E065FCFCFE0281A1",
							"examQuestionId": "57644",
							"optionName": "$\\left[ 0,1 \\right)\\cup \\left( 1,2 \\right]$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621AE0223E065FCFCFE0281A1",
							"examQuestionId": "57644",
							"optionName": "$\\left( 1,2 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由函数连续的定义知，选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91398",
					"paperId": "1816662617877135360",
					"questionId": "57654",
					"questionName": "若${f}'({{x}_{0}})=\\infty$，则下列结论正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D30223E065FCFCFE0281A1",
							"examQuestionId": "57654",
							"optionName": "函数$f(x)$在${{x}_{0}}$处是可导的",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325710223E065FCFCFE0281A1",
							"examQuestionId": "57654",
							"optionName": "曲线$y=f(x)$在点$\\left( {{x}_{0}},\\ f({{x}_{0}}) \\right)$处没有切线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A40F0223E065FCFCFE0281A1",
							"examQuestionId": "57654",
							"optionName": "曲线$y=f(x)$在点$\\left( {{x}_{0}},\\ f({{x}_{0}}) \\right)$处有平行于$x$轴的切线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622AD0223E065FCFCFE0281A1",
							"examQuestionId": "57654",
							"optionName": "曲线$y=f(x)$在点$\\left( {{x}_{0}},\\ f({{x}_{0}}) \\right)$处有垂直于$x$轴的切线",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "导数的几何意义",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91399",
					"paperId": "1816662617877135360",
					"questionId": "57719",
					"questionName": "函数$f(x)=x-\\ln x$的驻点是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6DF0223E065FCFCFE0281A1",
							"examQuestionId": "57719",
							"optionName": "$x=-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493257D0223E065FCFCFE0281A1",
							"examQuestionId": "57719",
							"optionName": "$x=-2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A41B0223E065FCFCFE0281A1",
							"examQuestionId": "57719",
							"optionName": "$x=1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B90223E065FCFCFE0281A1",
							"examQuestionId": "57719",
							"optionName": "$x=2$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=1-\\frac{1}{x}=\\frac{x-1}{x}$，由${f}'(x)=0$得C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91400",
					"paperId": "1816662617877135360",
					"questionId": "57650",
					"questionName": "函数$y={{x}^{2}}+1$在区间$\\left( -1\\,\\ 1 \\right)$内的最大值是（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7030223E065FCFCFE0281A1",
							"examQuestionId": "57650",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A10223E065FCFCFE0281A1",
							"examQuestionId": "57650",
							"optionName": "$1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A43F0223E065FCFCFE0281A1",
							"examQuestionId": "57650",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622DD0223E065FCFCFE0281A1",
							"examQuestionId": "57650",
							"optionName": "不存在",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由连续函数在闭区间上的性质知，选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91401",
					"paperId": "1816662617877135360",
					"questionId": "57691",
					"questionName": "若$f(x)={{e}^{x}}$,则${f}''(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3C40223E065FCFCFE0281A1",
							"examQuestionId": "57691",
							"optionName": "${{e}^{x}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322620223E065FCFCFE0281A1",
							"examQuestionId": "57691",
							"optionName": "$2{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1000223E065FCFCFE0281A1",
							"examQuestionId": "57691",
							"optionName": "$3{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F9E0223E065FCFCFE0281A1",
							"examQuestionId": "57691",
							"optionName": "$4{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=${{e}^{x}}$   ，  ${f}''(x)$=${{e}^{x}}$ 选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91402",
					"paperId": "1816662617877135360",
					"questionId": "57733",
					"questionName": "已知曲线$f\\left( x \\right)=\\frac{1}{x-1}$，则 下列结论正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A62F0223E065FCFCFE0281A1",
							"examQuestionId": "57733",
							"optionName": "直线$y=0$是曲线$f\\left( x \\right)=\\frac{1}{x-1}$的水平渐近线",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324CD0223E065FCFCFE0281A1",
							"examQuestionId": "57733",
							"optionName": "该曲线没有水平渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A36B0223E065FCFCFE0281A1",
							"examQuestionId": "57733",
							"optionName": "直线$x=0$是曲线$f\\left( x \\right)=\\frac{1}{x-1}$的铅直渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622090223E065FCFCFE0281A1",
							"examQuestionId": "57733",
							"optionName": "该曲线没有铅直渐近线",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由于 $\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,f\\left( x \\right)=0$，所以直线$y=0$是曲线的水平渐近线",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91403",
					"paperId": "1816662617877135360",
					"questionId": "57706",
					"questionName": "计算极限$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{3{{x}^{2}}-5x-7}{2{{x}^{2}}+x-11}$得（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3F60223E065FCFCFE0281A1",
							"examQuestionId": "57706",
							"optionName": "$\\frac{3}{2}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322940223E065FCFCFE0281A1",
							"examQuestionId": "57706",
							"optionName": "0",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1320223E065FCFCFE0281A1",
							"examQuestionId": "57706",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961FD00223E065FCFCFE0281A1",
							"examQuestionId": "57706",
							"optionName": "$-\\frac{3}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "通过两次洛必达法则可得$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{3{{x}^{2}}-5x-7}{2{{x}^{2}}+x-11}$$=\\frac{3}{2}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91404",
					"paperId": "1816662617877135360",
					"questionId": "57747",
					"questionName": "对曲线y = $\\frac{{{x}^{2}}}{2x-1}$来说，由$\\underset{x\\to \\frac{1}{2}}{\\mathop{\\text{lim}}}\\,\\frac{{{x}^{2}}}{2x-1}=\\infty $，以下说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6800223E065FCFCFE0281A1",
							"examQuestionId": "57747",
							"optionName": "曲线没有垂直渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493251E0223E065FCFCFE0281A1",
							"examQuestionId": "57747",
							"optionName": "曲线有垂直渐近线$x=-\\frac{1}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496225A0223E065FCFCFE0281A1",
							"examQuestionId": "57747",
							"optionName": "曲线有垂直渐近线$x=2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3BC0223E065FCFCFE0281A1",
							"examQuestionId": "57747",
							"optionName": "曲线有垂直渐近线$x=\\frac{1}{2}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由垂直渐近线的定义得选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91405",
					"paperId": "1816662617877135360",
					"questionId": "57687",
					"questionName": "若$y=f(x)$可导，其反函数为$x=\\varphi (y)$,则（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D80223E065FCFCFE0281A1",
							"examQuestionId": "57687",
							"optionName": "${f}'(x)$=${\\varphi }'(y)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325760223E065FCFCFE0281A1",
							"examQuestionId": "57687",
							"optionName": "${f}'(x)$=$\\frac{1}{{\\varphi }'(y)}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4140223E065FCFCFE0281A1",
							"examQuestionId": "57687",
							"optionName": "${f}'(x)$= $-{\\varphi }'(y)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B20223E065FCFCFE0281A1",
							"examQuestionId": "57687",
							"optionName": "${f}'(x)$=$-\\frac{1}{{\\varphi }'(y)}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "反函数求导公式，${f}'(x)$=$\\frac{1}{{\\varphi }'(y)}$， 选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91406",
					"paperId": "1816662617877135360",
					"questionId": "57605",
					"questionName": "函数$y=\\sqrt{16-{{x}^{2}}}+\\frac{x-1}{\\ln x}$的定义域是 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A68D0223E065FCFCFE0281A1",
							"examQuestionId": "57605",
							"optionName": "$\\left( 0,1 \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493252B0223E065FCFCFE0281A1",
							"examQuestionId": "57605",
							"optionName": "$\\left( 0,1 \\right)\\cup \\left( 1,4 \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3C90223E065FCFCFE0281A1",
							"examQuestionId": "57605",
							"optionName": "$\\left( 0,4 \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622670223E065FCFCFE0281A1",
							"examQuestionId": "57605",
							"optionName": "$\\left( 0,1 \\right)\\cup \\left( 1,4 \\right]$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\because \\left\\{ \\begin{matrix}   16-{{x}^{2}}\\ge 0  \\\\   \\lg x\\ne 0  \\\\   x>0  \\\\\\end{matrix} \\right.\\therefore \\left\\{ \\begin{matrix}   -4\\le x\\le 4  \\\\   x\\ne 1  \\\\   x>0  \\\\\\end{matrix} \\right.$    故选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91407",
					"paperId": "1816662617877135360",
					"questionId": "57615",
					"questionName": "函数$y=\\sqrt{\\text{5}-x}+\\ln (x-1)$的定义域是 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A45A0223E065FCFCFE0281A1",
							"examQuestionId": "57615",
							"optionName": "（0，5]",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322F80223E065FCFCFE0281A1",
							"examQuestionId": "57615",
							"optionName": "(1,5]",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1960223E065FCFCFE0281A1",
							"examQuestionId": "57615",
							"optionName": "(1,5)",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620340223E065FCFCFE0281A1",
							"examQuestionId": "57615",
							"optionName": "$(1,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\left\\{ \\begin{matrix}   \\text{5-}x\\ge 0  \\\\   x-1>0  \\\\\\end{matrix},\\left\\{ \\begin{matrix}   x\\le 5  \\\\   x>1  \\\\\\end{matrix} \\right. \\right.$ ,故选B。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91408",
					"paperId": "1816662617877135360",
					"questionId": "57661",
					"questionName": "$f(x)=\\sin x$,则${f}'(\\frac{\\pi }{4})=$ （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7060223E065FCFCFE0281A1",
							"examQuestionId": "57661",
							"optionName": "$\\cos x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A40223E065FCFCFE0281A1",
							"examQuestionId": "57661",
							"optionName": "$-\\cos x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4420223E065FCFCFE0281A1",
							"examQuestionId": "57661",
							"optionName": "$\\frac{\\sqrt{2}}{2}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E00223E065FCFCFE0281A1",
							"examQuestionId": "57661",
							"optionName": "$-\\frac{\\sqrt{2}}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(\\frac{\\pi }{4})=\\cos x{{|}_{x=\\frac{\\pi }{4}}}=\\frac{\\sqrt{2}}{2}$， 选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91409",
					"paperId": "1816662617877135360",
					"questionId": "57636",
					"questionName": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{n}){{}^{n+2}}=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7000223E065FCFCFE0281A1",
							"examQuestionId": "57636",
							"optionName": "${{e}^{2}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493259E0223E065FCFCFE0281A1",
							"examQuestionId": "57636",
							"optionName": "${{e}^{4}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A43C0223E065FCFCFE0281A1",
							"examQuestionId": "57636",
							"optionName": "${{e}^{3}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622DA0223E065FCFCFE0281A1",
							"examQuestionId": "57636",
							"optionName": "$e$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{n}){{}^{n+2}}=\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{n}){{}^{n}}\\cdot \\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{n}){{}^{2}}={{e}^{2\\times 1}}\\cdot {{(1+0)}^{2}}={{e}^{2}}$ ，故选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91410",
					"paperId": "1816662617877135360",
					"questionId": "57669",
					"questionName": "若$f(x)=\\sin \\text{ }x\\text{ }+\\text{ }{{e}^{x}}$ ,则${f}'(x)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A60E0223E065FCFCFE0281A1",
							"examQuestionId": "57669",
							"optionName": "$\\cos \\text{ }x\\text{ }+\\text{ }{{e}^{x}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324AC0223E065FCFCFE0281A1",
							"examQuestionId": "57669",
							"optionName": "$-\\cos \\text{ }x\\text{ }+\\text{ }{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A34A0223E065FCFCFE0281A1",
							"examQuestionId": "57669",
							"optionName": "$\\cos \\text{ }x\\text{ }-\\text{ }{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621E80223E065FCFCFE0281A1",
							"examQuestionId": "57669",
							"optionName": "$-\\cos \\text{ }x\\text{ }-\\text{ }{{e}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=\\cos \\text{ }x\\text{ }+\\text{ }{{e}^{x}}$，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91411",
					"paperId": "1816662617877135360",
					"questionId": "57673",
					"questionName": "若$f(x)$=$\\frac{\\sin x}{x}$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3BF0223E065FCFCFE0281A1",
							"examQuestionId": "57673",
							"optionName": "$\\frac{\\sin x-x}{{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493225D0223E065FCFCFE0281A1",
							"examQuestionId": "57673",
							"optionName": "$\\frac{\\cos x-x}{{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0FB0223E065FCFCFE0281A1",
							"examQuestionId": "57673",
							"optionName": "$\\frac{x\\cdot \\sin x-\\sin x}{{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F990223E065FCFCFE0281A1",
							"examQuestionId": "57673",
							"optionName": "$\\frac{x\\cdot \\cos x-\\sin x}{{{x}^{2}}}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=$\\frac{x\\cdot \\cos x-\\sin x}{{{x}^{2}}}$ ，选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91412",
					"paperId": "1816662617877135360",
					"questionId": "57630",
					"questionName": "下列各式中正确的是  （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A45D0223E065FCFCFE0281A1",
							"examQuestionId": "57630",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x}{\\sin x}=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322FB0223E065FCFCFE0281A1",
							"examQuestionId": "57630",
							"optionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{\\sin x}{x}=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1990223E065FCFCFE0281A1",
							"examQuestionId": "57630",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sin x}{x}=1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620370223E065FCFCFE0281A1",
							"examQuestionId": "57630",
							"optionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x}{\\sin x}=1$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由第一个重要极限知，选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91413",
					"paperId": "1816662617877135360",
					"questionId": "57657",
					"questionName": "若$f(x)$在${{x}_{0}}$处可导，则$f(x)$在${{x}_{0}}$处 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3BB0223E065FCFCFE0281A1",
							"examQuestionId": "57657",
							"optionName": "连续",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322590223E065FCFCFE0281A1",
							"examQuestionId": "57657",
							"optionName": "不连续",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0F70223E065FCFCFE0281A1",
							"examQuestionId": "57657",
							"optionName": "可能连续",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F950223E065FCFCFE0281A1",
							"examQuestionId": "57657",
							"optionName": "不可微",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由可导和可微及连续的关系知选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91414",
					"paperId": "1816662617877135360",
					"questionId": "57735",
					"questionName": "曲线y =${{x}^{2}}$－${{x}^{3}}$的凹区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A70C0223E065FCFCFE0281A1",
							"examQuestionId": "57735",
							"optionName": "$(-\\infty ,\\frac{1}{3})$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325AA0223E065FCFCFE0281A1",
							"examQuestionId": "57735",
							"optionName": "$(\\frac{1}{3},+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4480223E065FCFCFE0281A1",
							"examQuestionId": "57735",
							"optionName": "$(-\\infty ,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E60223E065FCFCFE0281A1",
							"examQuestionId": "57735",
							"optionName": "无",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=2x-3{{x}^{2}},{y}''=2-6x,{y}''=0\\text{ } x=\\frac{1}{3}$，当$x<\\frac{1}{3}$时,${y}''>0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91415",
					"paperId": "1816662617877135360",
					"questionId": "57670",
					"questionName": "若$f(x)=\\cos \\text{ }x\\text{ }+\\text{ }{{e}^{x}}$,则${f}'(0)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7080223E065FCFCFE0281A1",
							"examQuestionId": "57670",
							"optionName": "0",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A60223E065FCFCFE0281A1",
							"examQuestionId": "57670",
							"optionName": "1",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4440223E065FCFCFE0281A1",
							"examQuestionId": "57670",
							"optionName": "2",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E20223E065FCFCFE0281A1",
							"examQuestionId": "57670",
							"optionName": "3",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(0)=\\left( -\\sin \\text{ }x+{{e}^{x}} \\right)\\left| _{x=0} \\right.=\\left( 0+{{e}^{0}} \\right)=1$ ，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91416",
					"paperId": "1816662617877135360",
					"questionId": "57671",
					"questionName": "若$f(x)=\\sin \\text{ }x\\text{ }\\ln x$ ,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3BD0223E065FCFCFE0281A1",
							"examQuestionId": "57671",
							"optionName": "$\\cos \\text{ }x\\text{ }\\ln x+\\frac{\\sin x}{x}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493225B0223E065FCFCFE0281A1",
							"examQuestionId": "57671",
							"optionName": "$\\sin \\text{ }x\\text{ }\\ln x\\text{ }+\\frac{\\sin x}{x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0F90223E065FCFCFE0281A1",
							"examQuestionId": "57671",
							"optionName": "$\\cos \\text{ }x\\text{ }\\ln x-\\frac{\\sin x}{x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F970223E065FCFCFE0281A1",
							"examQuestionId": "57671",
							"optionName": "$\\sin \\text{ }x\\text{ }\\ln x\\text{ }-\\frac{\\sin x}{x}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=$\\cos \\text{ }x\\text{ }\\ln x+\\frac{\\sin x}{x}$ ，选A。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91417",
					"paperId": "1816662617877135360",
					"questionId": "57726",
					"questionName": "函数$f(x)=1-{{(x-2)}^{\\frac{2}{3}}}$的极大值是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A70A0223E065FCFCFE0281A1",
							"examQuestionId": "57726",
							"optionName": "$f(1)=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A80223E065FCFCFE0281A1",
							"examQuestionId": "57726",
							"optionName": "$f(0)=1-\\sqrt[3]{4}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4460223E065FCFCFE0281A1",
							"examQuestionId": "57726",
							"optionName": "$f(2)=1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E40223E065FCFCFE0281A1",
							"examQuestionId": "57726",
							"optionName": "不存在",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=-\\frac{2}{3}\\frac{1}{\\sqrt[3]{x-2}}$，在$(-\\infty ,2)$上,${f}'(x)>0$，在$(2,+\\infty )$上,${f}'(x)<0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91418",
					"paperId": "1816662617877135360",
					"questionId": "57713",
					"questionName": "以下运算中正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F50223E065FCFCFE0281A1",
							"examQuestionId": "57713",
							"optionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x+\\sin x}{x}=\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x+x}{x}=2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324930223E065FCFCFE0281A1",
							"examQuestionId": "57713",
							"optionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x+\\sin x}{x}=\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,{{\\left( \\frac{x+\\sin x}{x} \\right)}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3310223E065FCFCFE0281A1",
							"examQuestionId": "57713",
							"optionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x+\\sin x}{x}=\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{1}{x}\\sin x)=1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621CF0223E065FCFCFE0281A1",
							"examQuestionId": "57713",
							"optionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x+\\sin x}{x}=\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{1}{x}\\sin x)=1+1=2$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "C中利用了无穷小的性质",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91419",
					"paperId": "1816662617877135360",
					"questionId": "57610",
					"questionName": "函数$y={{3}^{x}}+2$的反函数是 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A59E0223E065FCFCFE0281A1",
							"examQuestionId": "57610",
							"optionName": "$y={{\\log }_{3}}x\\text{ }-2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493243C0223E065FCFCFE0281A1",
							"examQuestionId": "57610",
							"optionName": "$y={{\\log }_{3}}\\left( x-2 \\right)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2DA0223E065FCFCFE0281A1",
							"examQuestionId": "57610",
							"optionName": "$y={{\\log }_{3}}x+2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621780223E065FCFCFE0281A1",
							"examQuestionId": "57610",
							"optionName": "$~y={{\\log }_{3}}\\left( x+2 \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由$y={{3}^{x}}+2$ 有$y-2={{3}^{x}}$.从而有$x={{\\log }_{3}}\\left( y-2 \\right)$. 故选B.",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91420",
					"paperId": "1816662617877135360",
					"questionId": "57634",
					"questionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{x}){{}^{2x}}=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6FF0223E065FCFCFE0281A1",
							"examQuestionId": "57634",
							"optionName": "$e$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493259D0223E065FCFCFE0281A1",
							"examQuestionId": "57634",
							"optionName": "${{e}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A43B0223E065FCFCFE0281A1",
							"examQuestionId": "57634",
							"optionName": "$1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622D90223E065FCFCFE0281A1",
							"examQuestionId": "57634",
							"optionName": "${{e}^{4}}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,(1+\\frac{2}{x}){{}^{2x}}={{e}^{2\\times 2}}={{e}^{4}}$.故选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91421",
					"paperId": "1816662617877135360",
					"questionId": "57697",
					"questionName": "若$f(x)={{e}^{2x}}$,则${f}'(x)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F20223E065FCFCFE0281A1",
							"examQuestionId": "57697",
							"optionName": "${{e}^{2x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324900223E065FCFCFE0281A1",
							"examQuestionId": "57697",
							"optionName": "$2{{e}^{2x}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A32E0223E065FCFCFE0281A1",
							"examQuestionId": "57697",
							"optionName": "$3{{e}^{2x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621CC0223E065FCFCFE0281A1",
							"examQuestionId": "57697",
							"optionName": "$4{{e}^{2x}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)={{e}^{2x}}\\left( 2x \\right)'=2{{e}^{2x}}$ 选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91422",
					"paperId": "1816662617877135360",
					"questionId": "57662",
					"questionName": "若$f(x)=\\cos \\text{ }x$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A60C0223E065FCFCFE0281A1",
							"examQuestionId": "57662",
							"optionName": "$-\\sin x$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324AA0223E065FCFCFE0281A1",
							"examQuestionId": "57662",
							"optionName": "$~\\cos x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3480223E065FCFCFE0281A1",
							"examQuestionId": "57662",
							"optionName": "$\\sin x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621E60223E065FCFCFE0281A1",
							"examQuestionId": "57662",
							"optionName": "$~-\\cos x$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$$=-\\sin x$ ，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91423",
					"paperId": "1816662617877135360",
					"questionId": "57739",
					"questionName": "曲线y =${{x}^{3}}$的拐点是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A43A0223E065FCFCFE0281A1",
							"examQuestionId": "57739",
							"optionName": "$(0,0)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322D80223E065FCFCFE0281A1",
							"examQuestionId": "57739",
							"optionName": "$(1,1)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1760223E065FCFCFE0281A1",
							"examQuestionId": "57739",
							"optionName": "$(\\frac{1}{3},\\frac{1}{27})$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620140223E065FCFCFE0281A1",
							"examQuestionId": "57739",
							"optionName": "$(-1,-1)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=3{{x}^{2}},{y}''=6x,{y}''=0\\text{ } x=0$，当$x<0$时,${y}''<0$，当$x>0$时,${y}''>0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91424",
					"paperId": "1816662617877135360",
					"questionId": "57681",
					"questionName": "已知$f\\left( x \\right)={{e}^{\\frac{x}{3}}}$，则${f}'\\left( x \\right)=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5BE0223E065FCFCFE0281A1",
							"examQuestionId": "57681",
							"optionName": "$3{{e}^{\\frac{x}{3}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493245C0223E065FCFCFE0281A1",
							"examQuestionId": "57681",
							"optionName": "$\\frac{{{e}^{x}}}{3}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2FA0223E065FCFCFE0281A1",
							"examQuestionId": "57681",
							"optionName": "${{e}^{\\frac{x}{3}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621980223E065FCFCFE0281A1",
							"examQuestionId": "57681",
							"optionName": "$\\frac{{{e}^{\\frac{x}{3}}}}{3}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${{\\left( {{e}^{\\frac{x}{3}}} \\right)}^{\\prime }}={{e}^{\\frac{x}{3}}}{{\\left( \\frac{x}{3} \\right)}^{\\prime }}=\\frac{1}{3}{{e}^{\\frac{x}{3}}}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91425",
					"paperId": "1816662617877135360",
					"questionId": "57694",
					"questionName": "若$f(x)$在$x$处可导，则$df(x)=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6DA0223E065FCFCFE0281A1",
							"examQuestionId": "57694",
							"optionName": "${f}'(x)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325780223E065FCFCFE0281A1",
							"examQuestionId": "57694",
							"optionName": "${f}'(x)dx$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4160223E065FCFCFE0281A1",
							"examQuestionId": "57694",
							"optionName": "$-{f}'(x)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B40223E065FCFCFE0281A1",
							"examQuestionId": "57694",
							"optionName": "$-{f}'(x)dx$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$df(x)={f}'(x)dx$，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91426",
					"paperId": "1816662617877135360",
					"questionId": "57736",
					"questionName": "曲线y =${{x}^{2}}$－${{x}^{3}}$的拐点是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4760223E065FCFCFE0281A1",
							"examQuestionId": "57736",
							"optionName": "$(0,0)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323140223E065FCFCFE0281A1",
							"examQuestionId": "57736",
							"optionName": "$(1,1)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1B20223E065FCFCFE0281A1",
							"examQuestionId": "57736",
							"optionName": "$(\\frac{1}{3},\\frac{2}{27})$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620500223E065FCFCFE0281A1",
							"examQuestionId": "57736",
							"optionName": "该曲线无拐点",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=2x-3{{x}^{2}},{y}''=2-6x,{y}''=0\\text{ } x=\\frac{1}{3}$，当$x<\\frac{1}{3}$时,${y}''>0$，当$x>\\frac{1}{3}$时,${y}''<0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91427",
					"paperId": "1816662617877135360",
					"questionId": "57620",
					"questionName": "$f\\left( {{x}_{0}}+0 \\right)$与$f\\left( {{x}_{0}}-0 \\right)$都存在是函数$f\\left( x \\right)$在$x={{x}_{0}}$处有极限的是（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D60223E065FCFCFE0281A1",
							"examQuestionId": "57620",
							"optionName": "必要条件",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325740223E065FCFCFE0281A1",
							"examQuestionId": "57620",
							"optionName": "充分条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4120223E065FCFCFE0281A1",
							"examQuestionId": "57620",
							"optionName": "充要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B00223E065FCFCFE0281A1",
							"examQuestionId": "57620",
							"optionName": "无关条件",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由$x\\to {{x}_{0}}$时函数极限的定义知，选A。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91428",
					"paperId": "1816662617877135360",
					"questionId": "57677",
					"questionName": "若$f(x)=\\ln \\cos x$,则 ${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7360223E065FCFCFE0281A1",
							"examQuestionId": "57677",
							"optionName": "$-\\tan \\text{ }x$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D40223E065FCFCFE0281A1",
							"examQuestionId": "57677",
							"optionName": "$\\tan \\text{ }x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4720223E065FCFCFE0281A1",
							"examQuestionId": "57677",
							"optionName": "$-\\cot \\text{ }x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623100223E065FCFCFE0281A1",
							"examQuestionId": "57677",
							"optionName": "$\\cot \\text{ }x$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=\\frac{1}{\\cos x}\\cdot \\left( \\cos x \\right)'=$$-\\frac{\\sin x}{\\cos x}=-\\tan x$ ，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91429",
					"paperId": "1816662617877135360",
					"questionId": "57744",
					"questionName": "已知某函数一阶和二阶导数在区间$(1,+\\infty )$上${y}'>0$、 ${y}''>0$，则在区间$(1,+\\infty )$上函数图象的单调和凹凸情况是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A70F0223E065FCFCFE0281A1",
							"examQuestionId": "57744",
							"optionName": "单调增且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325AD0223E065FCFCFE0281A1",
							"examQuestionId": "57744",
							"optionName": "单调减且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A44B0223E065FCFCFE0281A1",
							"examQuestionId": "57744",
							"optionName": "单调减且凹",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E90223E065FCFCFE0281A1",
							"examQuestionId": "57744",
							"optionName": "单调增且凹",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "在$(1,+\\infty )$内，${y}'>0$，单调增加，${y}''>0$，凹的",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91430",
					"paperId": "1816662617877135360",
					"questionId": "57633",
					"questionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(x\\cdot \\cot 2x)=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5D00223E065FCFCFE0281A1",
							"examQuestionId": "57633",
							"optionName": "$\\frac{1}{2}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493246E0223E065FCFCFE0281A1",
							"examQuestionId": "57633",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A30C0223E065FCFCFE0281A1",
							"examQuestionId": "57633",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621AA0223E065FCFCFE0281A1",
							"examQuestionId": "57633",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,x\\cdot \\cot 2x=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x}{\\tan 2x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x}{2x}=\\frac{1}{2}$.故选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91431",
					"paperId": "1816662617877135360",
					"questionId": "57745",
					"questionName": "已知某函数一阶和二阶导数在区间$(1,2)$上的取值符号是${y}'<0$、${y}''<0$，则在区间$(1,2)$上函数图象的单调和凹凸情况是（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4780223E065FCFCFE0281A1",
							"examQuestionId": "57745",
							"optionName": "单调增且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323160223E065FCFCFE0281A1",
							"examQuestionId": "57745",
							"optionName": "单调减且凸",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1B40223E065FCFCFE0281A1",
							"examQuestionId": "57745",
							"optionName": "单调减且凹",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620520223E065FCFCFE0281A1",
							"examQuestionId": "57745",
							"optionName": "单调增且凹",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "在$(1,2)$内，${y}'<0$，单调减少，${y}''<0$，凸的",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91432",
					"paperId": "1816662617877135360",
					"questionId": "57746",
					"questionName": "对曲线y = $\\frac{2{{x}^{2}}}{{{x}^{2}}-1}$来说，由$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,y=\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{2{{x}^{2}}}{{{x}^{2}}-1}=2$，以下说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A67F0223E065FCFCFE0281A1",
							"examQuestionId": "57746",
							"optionName": "曲线没有水平渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493251D0223E065FCFCFE0281A1",
							"examQuestionId": "57746",
							"optionName": "曲线有水平渐近线$y=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3BB0223E065FCFCFE0281A1",
							"examQuestionId": "57746",
							"optionName": "曲线有水平渐近线$y=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622590223E065FCFCFE0281A1",
							"examQuestionId": "57746",
							"optionName": "曲线有水平渐近线$y=2$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由水平渐近线的定义得选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91433",
					"paperId": "1816662617877135360",
					"questionId": "57740",
					"questionName": "曲线 y = lnx的渐近线是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5550223E065FCFCFE0281A1",
							"examQuestionId": "57740",
							"optionName": "$y=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323F30223E065FCFCFE0281A1",
							"examQuestionId": "57740",
							"optionName": "$x=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496212F0223E065FCFCFE0281A1",
							"examQuestionId": "57740",
							"optionName": "无渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2910223E065FCFCFE0281A1",
							"examQuestionId": "57740",
							"optionName": "$x=0$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to {{0}^{+}}}{\\mathop{\\text{lim}}}\\,y=\\underset{x\\to {{0}^{+}}}{\\mathop{\\text{lim}}}\\,\\ln x=-\\infty $",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91434",
					"paperId": "1816662617877135360",
					"questionId": "57623",
					"questionName": "当$x\\to 1$时，下列变量中不是无穷小的是 （   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6920223E065FCFCFE0281A1",
							"examQuestionId": "57623",
							"optionName": "${{x}^{2}}-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325300223E065FCFCFE0281A1",
							"examQuestionId": "57623",
							"optionName": "$x\\left( x-2 \\right)+1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3CE0223E065FCFCFE0281A1",
							"examQuestionId": "57623",
							"optionName": "$3{{x}^{2}}-2x-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496226C0223E065FCFCFE0281A1",
							"examQuestionId": "57623",
							"optionName": "$4{{x}^{2}}-2x+1$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,(4{{x}^{2}}-2x+1)=4\\times 1-2\\times 1+1=3\\ne 0$ ，故选D。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91435",
					"paperId": "1816662617877135360",
					"questionId": "57640",
					"questionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{{{x}^{2}}}}-1}{\\cos x-1}=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D10223E065FCFCFE0281A1",
							"examQuestionId": "57640",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493256F0223E065FCFCFE0281A1",
							"examQuestionId": "57640",
							"optionName": "$-2$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A40D0223E065FCFCFE0281A1",
							"examQuestionId": "57640",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622AB0223E065FCFCFE0281A1",
							"examQuestionId": "57640",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{{{x}^{2}}}}-1}{\\cos x-1}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{x}^{2}}}{-\\frac{1}{2}{{x}^{2}}}=-2$ ，故选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91436",
					"paperId": "1816662617877135360",
					"questionId": "57702",
					"questionName": "利用洛必达法则求极限 $\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-{{e}^{-x}}-2x}{x-\\sin x}$时，以下做法正确的是（   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A73C0223E065FCFCFE0281A1",
							"examQuestionId": "57702",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-{{e}^{-x}}-2x}{x-\\sin x}$ $\\overset{\\frac{0}{0}}{\\mathop{=\\ }}\\,\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\left( {{e}^{x}}-{{e}^{-x}}-2x \\right){{\\,}^{\\prime }}}{\\left( x-\\sin x \\right){{\\,}^{\\prime }}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325DA0223E065FCFCFE0281A1",
							"examQuestionId": "57702",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-{{e}^{-x}}-2x}{x-\\sin x}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\left( \\frac{{{e}^{x}}-{{e}^{-x}}-2x}{x-\\sin x} \\right)}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4780223E065FCFCFE0281A1",
							"examQuestionId": "57702",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-{{e}^{-x}}-2x}{x-\\sin x}$ $\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( {{e}^{x}}-{{e}^{-x}}-2x \\right)}^{\\prime }}}{x-\\sin x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623160223E065FCFCFE0281A1",
							"examQuestionId": "57702",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-{{e}^{-x}}-2x}{x-\\sin x}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-{{e}^{-x}}-2x}{{{\\left( x-\\sin x \\right)}^{\\prime }}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "洛必达法则求极限的第一步是分子分母分别求导",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91437",
					"paperId": "1816662617877135360",
					"questionId": "57606",
					"questionName": "函数$y=\\frac{2x}{{{x}^{2}}-3x+2}$的定义域是 （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A68E0223E065FCFCFE0281A1",
							"examQuestionId": "57606",
							"optionName": "$\\left( -\\infty ,1 \\right)\\bigcup \\left( 1,2 \\right)\\bigcup \\left( 2,+\\infty \\right)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493252C0223E065FCFCFE0281A1",
							"examQuestionId": "57606",
							"optionName": "$\\left( -\\infty ,1 \\right)\\bigcup \\left( 1,+\\infty \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3CA0223E065FCFCFE0281A1",
							"examQuestionId": "57606",
							"optionName": "$\\left( -\\infty ,1 \\right)\\bigcup \\left( 2,+\\infty \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622680223E065FCFCFE0281A1",
							"examQuestionId": "57606",
							"optionName": "$\\left( -\\infty ,+\\infty \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${{x}^{2}}-3x+2\\ne 0.x-1\\left( x-2 \\right)\\ne 0$ 故选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91438",
					"paperId": "1816662617877135360",
					"questionId": "57608",
					"questionName": "设$F\\left( x \\right)={{a}^{x}}(a>0,a\\ne 1)$,那么$\\frac{F(x)}{F(y)}$= （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A59D0223E065FCFCFE0281A1",
							"examQuestionId": "57608",
							"optionName": "$F\\left( x+y \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493243B0223E065FCFCFE0281A1",
							"examQuestionId": "57608",
							"optionName": "$F\\left( x-y \\right)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2D90223E065FCFCFE0281A1",
							"examQuestionId": "57608",
							"optionName": "$F\\left( x \\right)\\cdot F\\left( y \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621770223E065FCFCFE0281A1",
							"examQuestionId": "57608",
							"optionName": "$F\\left( x \\right)-F\\left( y \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\frac{F(x)}{F(y)}=\\frac{{{a}^{x}}}{{{a}^{y}}}={{a}^{x-y}}.$故选B.",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91439",
					"paperId": "1816662617877135360",
					"questionId": "57607",
					"questionName": "设函数$f(x)=\\left\\{ \\begin{matrix}   x,x>0  \\\\   -x,x<0  \\\\\\end{matrix} \\right.$，那么$f(0)=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A68F0223E065FCFCFE0281A1",
							"examQuestionId": "57607",
							"optionName": "$-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493252D0223E065FCFCFE0281A1",
							"examQuestionId": "57607",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3CB0223E065FCFCFE0281A1",
							"examQuestionId": "57607",
							"optionName": "$1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622690223E065FCFCFE0281A1",
							"examQuestionId": "57607",
							"optionName": "无定义",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由定义知:应选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91440",
					"paperId": "1816662617877135360",
					"questionId": "57658",
					"questionName": "函数$f(x)=\\left| x \\right|$在$x=0$处（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3BC0223E065FCFCFE0281A1",
							"examQuestionId": "57658",
							"optionName": "连续但不可导",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493225A0223E065FCFCFE0281A1",
							"examQuestionId": "57658",
							"optionName": "连续且可导",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0F80223E065FCFCFE0281A1",
							"examQuestionId": "57658",
							"optionName": "不连续也不可导",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F960223E065FCFCFE0281A1",
							"examQuestionId": "57658",
							"optionName": "${f}'(0)=0$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "可导和连续的关系",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91441",
					"paperId": "1816662617877135360",
					"questionId": "57690",
					"questionName": "若$f(x)=3{{x}^{3}}-{{x}^{2}}+1$,则${f}''(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3C30223E065FCFCFE0281A1",
							"examQuestionId": "57690",
							"optionName": "$18x-2$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322610223E065FCFCFE0281A1",
							"examQuestionId": "57690",
							"optionName": "$18x-3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0FF0223E065FCFCFE0281A1",
							"examQuestionId": "57690",
							"optionName": "$18x+2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F9D0223E065FCFCFE0281A1",
							"examQuestionId": "57690",
							"optionName": "$18x+3$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=9{{x}^{2}}-2x$   ，${f}''(x)=18x-2$,选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91442",
					"paperId": "1816662617877135360",
					"questionId": "57700",
					"questionName": "若$dy={{e}^{x}}dx$,则$y=$ （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A73B0223E065FCFCFE0281A1",
							"examQuestionId": "57700",
							"optionName": "${{e}^{x}}+1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D90223E065FCFCFE0281A1",
							"examQuestionId": "57700",
							"optionName": "${{e}^{x}}+2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4770223E065FCFCFE0281A1",
							"examQuestionId": "57700",
							"optionName": "${{e}^{x}}-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623150223E065FCFCFE0281A1",
							"examQuestionId": "57700",
							"optionName": "${{e}^{x}}+C$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$d({{e}^{x}}+c)={{e}^{x}}dx$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91443",
					"paperId": "1816662617877135360",
					"questionId": "57696",
					"questionName": "设$y={{x}^{2}}$,则$dy{{|}_{x=3}}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F10223E065FCFCFE0281A1",
							"examQuestionId": "57696",
							"optionName": "6$dx$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493248F0223E065FCFCFE0281A1",
							"examQuestionId": "57696",
							"optionName": "3$dx$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A32D0223E065FCFCFE0281A1",
							"examQuestionId": "57696",
							"optionName": "2$dx$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621CB0223E065FCFCFE0281A1",
							"examQuestionId": "57696",
							"optionName": "4$dx$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=2x$ ， $dy{{|}_{x=3}}=6dx$  选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91444",
					"paperId": "1816662617877135360",
					"questionId": "57712",
					"questionName": "以下运算中正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7090223E065FCFCFE0281A1",
							"examQuestionId": "57712",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{x}^{2}}{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}=0\\cdot \\infty =0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A70223E065FCFCFE0281A1",
							"examQuestionId": "57712",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{x}^{2}}{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}}{\\frac{1}{{{x}^{2}}}}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\left( \\frac{{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}}{\\frac{1}{{{x}^{2}}}} \\right)}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4450223E065FCFCFE0281A1",
							"examQuestionId": "57712",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{x}^{2}}{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}}{\\frac{1}{{{x}^{2}}}}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}\\cdot (\\frac{1}{{{x}^{2}}}{)}'}{(\\frac{1}{{{x}^{2}}}{)}'}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E30223E065FCFCFE0281A1",
							"examQuestionId": "57712",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{x}^{2}}{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}}{\\frac{1}{{{x}^{2}}}}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}\\cdot (\\frac{1}{{{x}^{2}}}{)}'}{(\\frac{1}{{{x}^{2}}}{)}'}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\text{e}}^{\\frac{1}{{{x}^{2}}}}}=\\infty$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "A中结果错误，B中求导形式错误，C中最后一步错误",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91445",
					"paperId": "1816662617877135360",
					"questionId": "57720",
					"questionName": "函数$f(x)=x-\\ln x$的单调增区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A43E0223E065FCFCFE0281A1",
							"examQuestionId": "57720",
							"optionName": "$(0,1]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322DC0223E065FCFCFE0281A1",
							"examQuestionId": "57720",
							"optionName": "$[1,+\\infty )$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A17A0223E065FCFCFE0281A1",
							"examQuestionId": "57720",
							"optionName": "$[1,+\\infty )$和$(0,1]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620180223E065FCFCFE0281A1",
							"examQuestionId": "57720",
							"optionName": "$(0,+\\infty ]$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=1-\\frac{1}{x}=\\frac{x-1}{x}$，得驻点$x=1$，在$\\left( 1,+\\infty  \\right)$内,${f}'(x)>0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91446",
					"paperId": "1816662617877135360",
					"questionId": "57622",
					"questionName": "函数$f\\left( x \\right)=\\frac{1+{{x}^{3}}}{2{{x}^{3}}}$的图形的水平渐近线是（   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6910223E065FCFCFE0281A1",
							"examQuestionId": "57622",
							"optionName": "$y=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493252F0223E065FCFCFE0281A1",
							"examQuestionId": "57622",
							"optionName": "$y=-\\frac{\\text{1}}{\\text{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3CD0223E065FCFCFE0281A1",
							"examQuestionId": "57622",
							"optionName": "$y=\\frac{\\text{1}}{\\text{2}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496226B0223E065FCFCFE0281A1",
							"examQuestionId": "57622",
							"optionName": "$y=1$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{1+{{x}^{3}}}{2{{x}^{3}}}=\\frac{1}{2}$，故选C。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91447",
					"paperId": "1816662617877135360",
					"questionId": "57648",
					"questionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sqrt{1+{{x}^{2}}}-1}{x}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A49A0223E065FCFCFE0281A1",
							"examQuestionId": "57648",
							"optionName": "$1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323380223E065FCFCFE0281A1",
							"examQuestionId": "57648",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1D60223E065FCFCFE0281A1",
							"examQuestionId": "57648",
							"optionName": "$0$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620740223E065FCFCFE0281A1",
							"examQuestionId": "57648",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sqrt{1+{{x}^{2}}}-1}{x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{1+{{x}^{2}}-1}{x(\\sqrt{1+{{x}^{2}}}+1)}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x}{\\sqrt{1+{{x}^{2}}}+1}=0$ ，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91448",
					"paperId": "1816662617877135360",
					"questionId": "57689",
					"questionName": "若$x\\text{ }y+{{e}^{x}}-\\text{ }{{e}^{y}}=0$,则$\\frac{dy}{dx}\\left| _{_{\\begin{smallmatrix} x=0 \\\\ y=0 \\end{smallmatrix}}} \\right.=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3C20223E065FCFCFE0281A1",
							"examQuestionId": "57689",
							"optionName": "1",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322600223E065FCFCFE0281A1",
							"examQuestionId": "57689",
							"optionName": "2",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0FE0223E065FCFCFE0281A1",
							"examQuestionId": "57689",
							"optionName": "3",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F9C0223E065FCFCFE0281A1",
							"examQuestionId": "57689",
							"optionName": "4",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\left( x\\text{ }y+{{e}^{x}}-\\text{ }{{e}^{y}} \\right)&#39;=0$，则$y+x\\text{ }y&#39;+{{e}^{x}}-\\text{ }{{e}^{y}}y&#39;=0$，$y&#39;=$$\\frac{-e{}^{x}+y}{x-{{e}^{y}}}=\\frac{{{e}^{x}}+y}{{{e}^{y}}-x}$， $y&#39;\\left| _{_{\\begin{smallmatrix} x=0 \\\\ y=0 \\end{smallmatrix}}} \\right.=\\frac{{{e}^{0}}+0}{{{e}^{0}}-0}=1$，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91449",
					"paperId": "1816662617877135360",
					"questionId": "57699",
					"questionName": "若$dy=xdx$,则$y=$ （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F40223E065FCFCFE0281A1",
							"examQuestionId": "57699",
							"optionName": "$\\frac{1}{2}{{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324920223E065FCFCFE0281A1",
							"examQuestionId": "57699",
							"optionName": "$\\frac{1}{2}{{x}^{2}}+C$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3300223E065FCFCFE0281A1",
							"examQuestionId": "57699",
							"optionName": "${{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621CE0223E065FCFCFE0281A1",
							"examQuestionId": "57699",
							"optionName": "${{x}^{2}}+C$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$d(\\frac{1}{2}{{x}^{2}}+C)=xdx$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91450",
					"paperId": "1816662617877135360",
					"questionId": "57715",
					"questionName": "函数$f(x)=2{{x}^{3}}-6{{x}^{2}}-18x-7$的单调增区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F70223E065FCFCFE0281A1",
							"examQuestionId": "57715",
							"optionName": "$(-\\infty ,-1]$和$\\left[ -1,3 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324950223E065FCFCFE0281A1",
							"examQuestionId": "57715",
							"optionName": "$[3,+\\infty )$和$\\left[ -1,3 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3330223E065FCFCFE0281A1",
							"examQuestionId": "57715",
							"optionName": "$(-\\infty ,-1]$和$[3,+\\infty )$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621D10223E065FCFCFE0281A1",
							"examQuestionId": "57715",
							"optionName": "$\\left[ -1,3 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=6{{x}^{2}}-12x-18=6(x+1)(x-3)$，由${f}'(x)=0$得驻点${{x}_{1}}=-1,{{x}_{2}}=3,$在$\\left( -\\infty ,-1 \\right),\\left( 3,+\\infty  \\right)$上,${f}'(x)>0$，得C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91451",
					"paperId": "1816662617877135360",
					"questionId": "57742",
					"questionName": "已知某函数一阶和二阶导数在区间$(0,1)$上，${y}'>0$、${y}''<0$，则在区间$(0,1)$上其图象的单调和凹凸情况是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A70E0223E065FCFCFE0281A1",
							"examQuestionId": "57742",
							"optionName": "单调增且凸",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325AC0223E065FCFCFE0281A1",
							"examQuestionId": "57742",
							"optionName": "单调减且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A44A0223E065FCFCFE0281A1",
							"examQuestionId": "57742",
							"optionName": "单调减且凹",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E80223E065FCFCFE0281A1",
							"examQuestionId": "57742",
							"optionName": "单调增且凹",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "在$(0,1)$内，${y}'>0$，单调增加，${y}''<0$，凸的",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91452",
					"paperId": "1816662617877135360",
					"questionId": "57743",
					"questionName": "已知某函数一阶和二阶导数在区间$(-\\sqrt{3},-1)$上，${y}'<0$、${y}''>0$，则在区间$(-\\sqrt{3},-1)$上函数图象的单调和凹凸情况是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4770223E065FCFCFE0281A1",
							"examQuestionId": "57743",
							"optionName": "单调增且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323150223E065FCFCFE0281A1",
							"examQuestionId": "57743",
							"optionName": "单调减且凸",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1B30223E065FCFCFE0281A1",
							"examQuestionId": "57743",
							"optionName": "单调减且凹",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620510223E065FCFCFE0281A1",
							"examQuestionId": "57743",
							"optionName": "单调增且凹",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "在$(-\\sqrt{3},-1)$内，${y}'<0$，单调减少，${y}''>0$，凹的",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91453",
					"paperId": "1816662617877135360",
					"questionId": "57612",
					"questionName": "由$y=\\sqrt{u},u=2+{{v}^{2}},v=\\cos x$复合而成的复合函数是（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A59F0223E065FCFCFE0281A1",
							"examQuestionId": "57612",
							"optionName": "$y=\\sqrt{\\text{2}+\\cos x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493243D0223E065FCFCFE0281A1",
							"examQuestionId": "57612",
							"optionName": "$y=\\sqrt{\\text{2}+\\text{co}{{\\text{s}}^{\\text{2}}}x}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2DB0223E065FCFCFE0281A1",
							"examQuestionId": "57612",
							"optionName": "$y=2+{{\\cos }^{2}}x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621790223E065FCFCFE0281A1",
							"examQuestionId": "57612",
							"optionName": "$y=2+\\sqrt{\\cos x}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由复合函数的概念知，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91454",
					"paperId": "1816662617877135360",
					"questionId": "57614",
					"questionName": "设$f\\left( x \\right)={{e}^{2}}$,则$f\\left( x+2 \\right)-f\\left( x+1 \\right)=$ （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4590223E065FCFCFE0281A1",
							"examQuestionId": "57614",
							"optionName": "${{e}^{3}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322F70223E065FCFCFE0281A1",
							"examQuestionId": "57614",
							"optionName": "$e$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1950223E065FCFCFE0281A1",
							"examQuestionId": "57614",
							"optionName": "$0$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620330223E065FCFCFE0281A1",
							"examQuestionId": "57614",
							"optionName": "${{\\text{e}}^{\\frac{x+2}{x+1}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$f\\left( x+2 \\right)-f\\left( x+1 \\right)={{e}^{2}}-{{e}^{2}}=0$ . 故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91455",
					"paperId": "1816662617877135360",
					"questionId": "57618",
					"questionName": "数列$\\{{{x}_{n}}\\}$有界是数列$\\{{{x}_{n}}\\}$收敛的（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D50223E065FCFCFE0281A1",
							"examQuestionId": "57618",
							"optionName": "必要条件",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325730223E065FCFCFE0281A1",
							"examQuestionId": "57618",
							"optionName": "充分条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4110223E065FCFCFE0281A1",
							"examQuestionId": "57618",
							"optionName": "充要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622AF0223E065FCFCFE0281A1",
							"examQuestionId": "57618",
							"optionName": "无关条件",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由收敛数列的性质知，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91456",
					"paperId": "1816662617877135360",
					"questionId": "57637",
					"questionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{(1+4x)}^{\\frac{1}{x}}}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5D20223E065FCFCFE0281A1",
							"examQuestionId": "57637",
							"optionName": "${{e}^{-\\,4}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324700223E065FCFCFE0281A1",
							"examQuestionId": "57637",
							"optionName": "${{e}^{4}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A30E0223E065FCFCFE0281A1",
							"examQuestionId": "57637",
							"optionName": "${{\\text{e}}^{\\frac{1}{4}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621AC0223E065FCFCFE0281A1",
							"examQuestionId": "57637",
							"optionName": "${{e}^{-\\,\\frac{1}{4}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{(1+4x)}^{\\frac{1}{x}}}={{e}^{4}}$ ，故选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91457",
					"paperId": "1816662617877135360",
					"questionId": "57642",
					"questionName": "函数$f\\left( x \\right)$在${{x}_{0}}$处连续是$f\\left( x \\right)$在${{x}_{0}}$处有定义的（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5D30223E065FCFCFE0281A1",
							"examQuestionId": "57642",
							"optionName": "必要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324710223E065FCFCFE0281A1",
							"examQuestionId": "57642",
							"optionName": "充分条件",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A30F0223E065FCFCFE0281A1",
							"examQuestionId": "57642",
							"optionName": "充要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621AD0223E065FCFCFE0281A1",
							"examQuestionId": "57642",
							"optionName": "无关条件",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由函数连续的定义知，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91458",
					"paperId": "1816662617877135360",
					"questionId": "57647",
					"questionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,{{e}^{\\frac{1}{x}}}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4990223E065FCFCFE0281A1",
							"examQuestionId": "57647",
							"optionName": "$1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323370223E065FCFCFE0281A1",
							"examQuestionId": "57647",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1D50223E065FCFCFE0281A1",
							"examQuestionId": "57647",
							"optionName": "$-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620730223E065FCFCFE0281A1",
							"examQuestionId": "57647",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,{{e}^{\\frac{1}{x}}}={{e}^{0}}=1$ ，故选 A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91459",
					"paperId": "1816662617877135360",
					"questionId": "57659",
					"questionName": "曲线$y={{x}^{2}}-x$在$x=1$处的切线方程为（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7050223E065FCFCFE0281A1",
							"examQuestionId": "57659",
							"optionName": "$y=x-1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A30223E065FCFCFE0281A1",
							"examQuestionId": "57659",
							"optionName": "$y=x-2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4410223E065FCFCFE0281A1",
							"examQuestionId": "57659",
							"optionName": "$y=x+1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622DF0223E065FCFCFE0281A1",
							"examQuestionId": "57659",
							"optionName": "$y=x+2$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$k={y}'\\left| _{x=1}= \\right.\\left( 2x-1 \\right){{|}_{x=1}}=1$ ，切线为 $y-0=x-1$， 即 $y=x-1$ ，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91460",
					"paperId": "1816662617877135360",
					"questionId": "57679",
					"questionName": "若$f(x)=\\sin \\sqrt{x}$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5BC0223E065FCFCFE0281A1",
							"examQuestionId": "57679",
							"optionName": "$\\cos \\sqrt{x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493245A0223E065FCFCFE0281A1",
							"examQuestionId": "57679",
							"optionName": "$\\frac{1}{2\\sqrt{x}}\\cdot \\cos \\sqrt{x}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2F80223E065FCFCFE0281A1",
							"examQuestionId": "57679",
							"optionName": "$\\frac{\\text{1}}{\\sqrt{x}}\\cdot \\cos \\sqrt{x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621960223E065FCFCFE0281A1",
							"examQuestionId": "57679",
							"optionName": "$\\frac{\\text{1}}{\\text{2}}\\cos \\sqrt{x}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=${f}'(x)=\\cos \\sqrt{x}\\cdot \\sqrt{x}'=\\frac{1}{2\\sqrt{x}}\\cdot \\cos \\sqrt{x}$ ， 选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91461",
					"paperId": "1816662617877135360",
					"questionId": "57705",
					"questionName": "计算极限$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{\\ln x}{x-1}$，结果正确的是（    ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3F50223E065FCFCFE0281A1",
							"examQuestionId": "57705",
							"optionName": "$0$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322930223E065FCFCFE0281A1",
							"examQuestionId": "57705",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1310223E065FCFCFE0281A1",
							"examQuestionId": "57705",
							"optionName": "1",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961FCF0223E065FCFCFE0281A1",
							"examQuestionId": "57705",
							"optionName": "$-1$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{\\ln x}{x-1}$$\\overset{\\frac{\\infty }{\\infty }}{\\mathop{=}}\\,\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( \\ln x \\right)}^{\\prime }}}{{{\\left( x-1 \\right)}^{\\prime }}}$$=\\underset{x\\to +\\infty }{\\mathop{\\text{lim}}}\\,\\frac{\\frac{1}{x}}{1}=0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91462",
					"paperId": "1816662617877135360",
					"questionId": "57727",
					"questionName": "关于函数$y={{x}^{3}}$，下列说法正确的是（   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4730223E065FCFCFE0281A1",
							"examQuestionId": "57727",
							"optionName": "函数$y={{x}^{3}}$在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$ 上单调增加",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323110223E065FCFCFE0281A1",
							"examQuestionId": "57727",
							"optionName": "曲线$y={{x}^{3}}$没有拐点",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1AF0223E065FCFCFE0281A1",
							"examQuestionId": "57727",
							"optionName": "函数$y={{x}^{3}}$在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$ 上单调减少",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496204D0223E065FCFCFE0281A1",
							"examQuestionId": "57727",
							"optionName": "$x=0$是函数$y={{x}^{3}}$的极小点",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=3{{x}^{2}}>0$所以单调增加",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91463",
					"paperId": "1816662617877135360",
					"questionId": "57653",
					"questionName": "若$f(x)$在$x\\text{=}1$处可导，则下列结论正确的是 （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A60A0223E065FCFCFE0281A1",
							"examQuestionId": "57653",
							"optionName": "${f}'(1)=f(x)\\left| _{x=1} \\right.$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324A80223E065FCFCFE0281A1",
							"examQuestionId": "57653",
							"optionName": "${f}'(1)=\\left[ f(1) \\right]{{}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3460223E065FCFCFE0281A1",
							"examQuestionId": "57653",
							"optionName": "${f}'(1)$表示函数$f(x)$在$x\\text{=}1$处的瞬时变化率",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621E40223E065FCFCFE0281A1",
							"examQuestionId": "57653",
							"optionName": "${f}'(1)$表示函数$f(x)$在某区间上的平均变化率",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "导数的意义",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91464",
					"paperId": "1816662617877135360",
					"questionId": "57628",
					"questionName": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{{(x+1)}{{}^{3}}-{{(x-2)}^{3}}}{{{x}^{2}}+2x+3}=$ （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5CF0223E065FCFCFE0281A1",
							"examQuestionId": "57628",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493246D0223E065FCFCFE0281A1",
							"examQuestionId": "57628",
							"optionName": "$-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A30B0223E065FCFCFE0281A1",
							"examQuestionId": "57628",
							"optionName": "$9$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621A90223E065FCFCFE0281A1",
							"examQuestionId": "57628",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x+1{{}^{3}}-{{(x-2)}^{3}}}{{{x}^{2}}+2x+3}=\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{9{{x}^{2}}-9x+9}{{{x}^{2}}+2x+3}=9$.故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91465",
					"paperId": "1816662617877135360",
					"questionId": "57643",
					"questionName": "“函数$f\\left( x \\right)$在点${{x}_{0}}$处有定义”是“$f\\left( x \\right)$在${{x}_{0}}$处连续”的（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7010223E065FCFCFE0281A1",
							"examQuestionId": "57643",
							"optionName": "必要条件",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493259F0223E065FCFCFE0281A1",
							"examQuestionId": "57643",
							"optionName": "充分条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A43D0223E065FCFCFE0281A1",
							"examQuestionId": "57643",
							"optionName": "充要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622DB0223E065FCFCFE0281A1",
							"examQuestionId": "57643",
							"optionName": "无关条件",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由函数连续的定义知，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91466",
					"paperId": "1816662617877135360",
					"questionId": "57652",
					"questionName": "若$f(x)$在$x=2$处可导，则${f}'(2)$= （ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7040223E065FCFCFE0281A1",
							"examQuestionId": "57652",
							"optionName": "$\\underset{x\\to 2}{\\mathop{\\text{lim}}}\\,\\frac{f(x)-f(2)}{x-2}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A20223E065FCFCFE0281A1",
							"examQuestionId": "57652",
							"optionName": "$\\underset{x\\to 2}{\\mathop{\\text{lim}}}\\,\\frac{f(x)+f(2)}{x-2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4400223E065FCFCFE0281A1",
							"examQuestionId": "57652",
							"optionName": "$\\underset{x\\to 2}{\\mathop{\\text{lim}}}\\,\\frac{f(2)-f(x)}{x-2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622DE0223E065FCFCFE0281A1",
							"examQuestionId": "57652",
							"optionName": "$\\underset{x\\to 2}{\\mathop{\\text{lim}}}\\,\\frac{f(x)}{f(2)}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由导数定义，${f}'(2)$=$\\underset{x\\to 2}{\\mathop{\\text{lim}}}\\,\\frac{f(x)-f(2)}{x-2}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91467",
					"paperId": "1816662617877135360",
					"questionId": "57668",
					"questionName": "若$f(x)$$={{3}^{x}}$ ,则${f}'(x)$=（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7070223E065FCFCFE0281A1",
							"examQuestionId": "57668",
							"optionName": "${{3}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A50223E065FCFCFE0281A1",
							"examQuestionId": "57668",
							"optionName": "${{3}^{x}}ln3$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4430223E065FCFCFE0281A1",
							"examQuestionId": "57668",
							"optionName": "$\\frac{1}{{{3}^{x}}}\\ln 3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622E10223E065FCFCFE0281A1",
							"examQuestionId": "57668",
							"optionName": "$\\frac{1}{\\ln 3}{{3}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=3xln3，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91468",
					"paperId": "1816662617877135360",
					"questionId": "57750",
					"questionName": "对曲线y = $\\frac{x}{3-{{x}^{2}}}$来说，由$\\underset{x\\to \\sqrt{3}}{\\mathop{\\text{lim}}}\\,\\frac{x}{3-{{x}^{2}}}=\\infty $，$\\underset{x\\to -\\sqrt{3}}{\\mathop{\\text{lim}}}\\,\\frac{x}{3-{{x}^{2}}}=\\infty $，以下说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4790223E065FCFCFE0281A1",
							"examQuestionId": "57750",
							"optionName": "曲线有两条垂直渐近线$x=3$和$x=-3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323170223E065FCFCFE0281A1",
							"examQuestionId": "57750",
							"optionName": "曲线有两条垂直渐近线$y=3$和$y=-3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1B50223E065FCFCFE0281A1",
							"examQuestionId": "57750",
							"optionName": "曲线有两条垂直渐近线$x=\\sqrt{3}$和$x=-\\sqrt{3}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620530223E065FCFCFE0281A1",
							"examQuestionId": "57750",
							"optionName": "曲线有两条垂直渐近线$y=\\sqrt{3}$和$y=-\\sqrt{3}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由垂直渐近线的定义得选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91469",
					"paperId": "1816662617877135360",
					"questionId": "57641",
					"questionName": "函数$f\\left( x \\right)=5{{x}^{2}}$自变量$x$有增量$\\Delta x$时，函数$f\\left( x \\right)$的相应增量$\\Delta y$= （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D20223E065FCFCFE0281A1",
							"examQuestionId": "57641",
							"optionName": "$10x\\Delta x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325700223E065FCFCFE0281A1",
							"examQuestionId": "57641",
							"optionName": "$10+5\\Delta x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A40E0223E065FCFCFE0281A1",
							"examQuestionId": "57641",
							"optionName": "$10x\\Delta x+5{{\\left( \\Delta x \\right)}^{2}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622AC0223E065FCFCFE0281A1",
							"examQuestionId": "57641",
							"optionName": "$10\\Delta x+{{\\left( \\Delta x \\right)}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\Delta y=5{{(x+\\Delta x)}^{2}}-5{{x}^{2}}=10x\\cdot \\Delta x+5{{(\\Delta x)}^{2}}$ ，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91470",
					"paperId": "1816662617877135360",
					"questionId": "57655",
					"questionName": "设物体的运动规律是$s={{t}^{3}}+2{{t}^{2}}+5\\ (m)$,则物体在$t=1\\ \\left( s \\right)$时速度为（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3B90223E065FCFCFE0281A1",
							"examQuestionId": "57655",
							"optionName": "5m/s",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322570223E065FCFCFE0281A1",
							"examQuestionId": "57655",
							"optionName": "6m/s",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0F50223E065FCFCFE0281A1",
							"examQuestionId": "57655",
							"optionName": "7m/s",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F930223E065FCFCFE0281A1",
							"examQuestionId": "57655",
							"optionName": "8m/s",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由$s'\\left( t \\right)=3{{t}^{2}}+4t,$所以$s'{{|}_{t=1}}=7m/s$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91471",
					"paperId": "1816662617877135360",
					"questionId": "57732",
					"questionName": "已知函数 $f\\left( x \\right)=\\frac{{{x}^{3}}}{3}-{{x}^{2}}+2$ ，则下列结论错误的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A62E0223E065FCFCFE0281A1",
							"examQuestionId": "57732",
							"optionName": "${f}'\\left( 0 \\right)=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324CC0223E065FCFCFE0281A1",
							"examQuestionId": "57732",
							"optionName": "${f}''\\left( 0 \\right)<0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A36A0223E065FCFCFE0281A1",
							"examQuestionId": "57732",
							"optionName": "$f\\left( 0 \\right)$是$f\\left( x \\right)$的极小值",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622080223E065FCFCFE0281A1",
							"examQuestionId": "57732",
							"optionName": "$f\\left( 0 \\right)$是$f\\left( x \\right)$的极大值",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'\\left( x \\right)={{x}^{2}}-2x=x(x-2),x<0,{y}'>0,x>0,{y}'<0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91472",
					"paperId": "1816662617877135360",
					"questionId": "57621",
					"questionName": "设$f(x)=$$\\left\\{ \\begin{matrix}   3x+2,x\\le 0  \\\\   {{x}^{2}}-2,x>0  \\\\\\end{matrix} \\right.$,则$\\underset{x\\to 0+0}{\\mathop{\\text{lim}}}\\,f(x)$= （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6900223E065FCFCFE0281A1",
							"examQuestionId": "57621",
							"optionName": "2",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493252E0223E065FCFCFE0281A1",
							"examQuestionId": "57621",
							"optionName": "-2",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3CC0223E065FCFCFE0281A1",
							"examQuestionId": "57621",
							"optionName": "-1",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496226A0223E065FCFCFE0281A1",
							"examQuestionId": "57621",
							"optionName": "0",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0+0}{\\mathop{\\text{lim}}}\\,f(x)=\\underset{x\\to 0+0}{\\mathop{\\text{lim}}}\\,({{x}^{2}}-2)={{0}^{2}}-2=-2$，选B。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91473",
					"paperId": "1816662617877135360",
					"questionId": "57675",
					"questionName": "若$f(x)=$${{\\text{e}}^{{{x}^{2}}}}$,则${f}'(x)=$（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7350223E065FCFCFE0281A1",
							"examQuestionId": "57675",
							"optionName": "$2\\cdot {{e}^{{{x}^{2}}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D30223E065FCFCFE0281A1",
							"examQuestionId": "57675",
							"optionName": "$2x\\cdot {{e}^{{{x}^{2}}}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4710223E065FCFCFE0281A1",
							"examQuestionId": "57675",
							"optionName": "${{x}^{2}}\\cdot {{e}^{{{x}^{2}}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496230F0223E065FCFCFE0281A1",
							"examQuestionId": "57675",
							"optionName": "$x\\cdot {{e}^{{{x}^{2}}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)$=${{e}^{{{x}^{2}}}}\\cdot \\left( {{x}^{2}} \\right)'=2x\\cdot {{e}^{{{x}^{2}}}}$ ，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91474",
					"paperId": "1816662617877135360",
					"questionId": "57716",
					"questionName": "函数$f(x)=2{{x}^{3}}-6{{x}^{2}}-18x-7$的单调减区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F80223E065FCFCFE0281A1",
							"examQuestionId": "57716",
							"optionName": "$(-\\infty ,-1]$和$\\left[ -1,3 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324960223E065FCFCFE0281A1",
							"examQuestionId": "57716",
							"optionName": "$[3,+\\infty )$和$\\left[ -1,3 \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3340223E065FCFCFE0281A1",
							"examQuestionId": "57716",
							"optionName": "$(-\\infty ,-1]$和$[3,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621D20223E065FCFCFE0281A1",
							"examQuestionId": "57716",
							"optionName": "$\\left[ -1,3 \\right]$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=6{{x}^{2}}-12x-18=6(x+1)(x-3)$，由${f}'(x)=0$得驻点${{x}_{1}}=-1,{{x}_{2}}=3,$在$\\left( -1,3 \\right)$上${f}'(x)<0$，得D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91475",
					"paperId": "1816662617877135360",
					"questionId": "57721",
					"questionName": "函数$f(x)=x-\\ln x$的单调减区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3F90223E065FCFCFE0281A1",
							"examQuestionId": "57721",
							"optionName": "$(0,1]$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322970223E065FCFCFE0281A1",
							"examQuestionId": "57721",
							"optionName": "$[1,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1350223E065FCFCFE0281A1",
							"examQuestionId": "57721",
							"optionName": "$[1,+\\infty )$和$(0,1]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961FD30223E065FCFCFE0281A1",
							"examQuestionId": "57721",
							"optionName": "$(0,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}&#39;(x)=1-\\frac{1}{x}=\\frac{x-1}{x}$，得驻点$x=1$，在$\\left( 0,1 \\right)$上,${f}&#39;(x)&lt;0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91476",
					"paperId": "1816662617877135360",
					"questionId": "57749",
					"questionName": "对曲线y = $\\frac{x}{3-{{x}^{2}}}$来说，由$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{x}{3-{{x}^{2}}}=0$，以下说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6820223E065FCFCFE0281A1",
							"examQuestionId": "57749",
							"optionName": "曲线没有水平渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325200223E065FCFCFE0281A1",
							"examQuestionId": "57749",
							"optionName": "曲线有水平渐近线$y=\\sqrt{3}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3BE0223E065FCFCFE0281A1",
							"examQuestionId": "57749",
							"optionName": "曲线有水平渐近线$y=-\\sqrt{3}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496225C0223E065FCFCFE0281A1",
							"examQuestionId": "57749",
							"optionName": "曲线有水平渐近线$y=0$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由水平渐近线的定义可得",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91477",
					"paperId": "1816662617877135360",
					"questionId": "57632",
					"questionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(x\\sin \\frac{1}{x}+\\frac{1}{x}\\sin x)=$（   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4970223E065FCFCFE0281A1",
							"examQuestionId": "57632",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323350223E065FCFCFE0281A1",
							"examQuestionId": "57632",
							"optionName": "$1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1D30223E065FCFCFE0281A1",
							"examQuestionId": "57632",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620710223E065FCFCFE0281A1",
							"examQuestionId": "57632",
							"optionName": "不存在",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(x\\sin \\frac{1}{x}+\\frac{1}{x}\\sin x)=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,x\\cdot \\sin \\frac{1}{x}+\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sin x}{x}=0+1=1$.故选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91478",
					"paperId": "1816662617877135360",
					"questionId": "57649",
					"questionName": "设函数$f(x)=\\left\\{ \\begin{matrix}   {{e}^{x}},\\quad \\ x<0  \\\\   a+x,\\quad x\\ge 0  \\\\\\end{matrix} \\right.$是（-$\\infty $，+$\\infty $）上的连续函数，则$a=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A49B0223E065FCFCFE0281A1",
							"examQuestionId": "57649",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323390223E065FCFCFE0281A1",
							"examQuestionId": "57649",
							"optionName": "$1$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1D70223E065FCFCFE0281A1",
							"examQuestionId": "57649",
							"optionName": "$-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620750223E065FCFCFE0281A1",
							"examQuestionId": "57649",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由函数连续的条件知，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91479",
					"paperId": "1816662617877135360",
					"questionId": "57683",
					"questionName": "已知$f\\left( x \\right)={{\\cos }^{2}}x$，则${f}'\\left( x \\right)=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F00223E065FCFCFE0281A1",
							"examQuestionId": "57683",
							"optionName": "$2\\cos x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493248E0223E065FCFCFE0281A1",
							"examQuestionId": "57683",
							"optionName": "$2\\sin x\\cos x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A32C0223E065FCFCFE0281A1",
							"examQuestionId": "57683",
							"optionName": "$-2\\sin x\\cos x$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621CA0223E065FCFCFE0281A1",
							"examQuestionId": "57683",
							"optionName": "$2x\\sin {{x}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${{\\left( {{\\cos }^{2}}x \\right)}^{\\prime }}=2\\cos x{{\\left( \\cos x \\right)}^{\\prime }}=2\\cos x\\left( -\\sin x \\right)=-2\\sin x\\cos x$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91480",
					"paperId": "1816662617877135360",
					"questionId": "57724",
					"questionName": "函数$f(x)=1-{{(x-2)}^{\\frac{2}{3}}}$的单调减区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4380223E065FCFCFE0281A1",
							"examQuestionId": "57724",
							"optionName": "$[2,+\\infty )$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322D60223E065FCFCFE0281A1",
							"examQuestionId": "57724",
							"optionName": "$(-\\infty ,2]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1740223E065FCFCFE0281A1",
							"examQuestionId": "57724",
							"optionName": "$(-\\infty ,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620120223E065FCFCFE0281A1",
							"examQuestionId": "57724",
							"optionName": "不存在",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=-\\frac{2}{3}\\frac{1}{\\sqrt[3]{x-2}}$，在$(2,+\\infty )$上,${f}'(x)<0$，在$[2,+\\infty )$上单调递减",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91481",
					"paperId": "1816662617877135360",
					"questionId": "57748",
					"questionName": "对曲线y = $\\frac{1}{\\mathrm{2}}{{\\mathrm{e}}^{-\\frac{{{x}^{2}}}{2}}}$来说，由$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{1}{2}{{\\text{e}}^{-\\frac{{{x}^{2}}}{2}}}=0$，以下说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6810223E065FCFCFE0281A1",
							"examQuestionId": "57748",
							"optionName": "曲线没有水平渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493251F0223E065FCFCFE0281A1",
							"examQuestionId": "57748",
							"optionName": "曲线有水平渐近线$y=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3BD0223E065FCFCFE0281A1",
							"examQuestionId": "57748",
							"optionName": "曲线有水平渐近线$y=-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496225B0223E065FCFCFE0281A1",
							"examQuestionId": "57748",
							"optionName": "曲线有水平渐近线$y=0$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由水平渐近线的定义可得D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91482",
					"paperId": "1816662617877135360",
					"questionId": "57680",
					"questionName": "已知$f\\left( x \\right)=\\sqrt{2x+3}$，则${f}'\\left( x \\right)=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5BD0223E065FCFCFE0281A1",
							"examQuestionId": "57680",
							"optionName": "$\\frac{1}{\\sqrt{2x+3}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493245B0223E065FCFCFE0281A1",
							"examQuestionId": "57680",
							"optionName": "$-\\frac{1}{\\sqrt{2x+3}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2F90223E065FCFCFE0281A1",
							"examQuestionId": "57680",
							"optionName": "${{\\left( 2x+3 \\right)}^{\\frac{3}{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621970223E065FCFCFE0281A1",
							"examQuestionId": "57680",
							"optionName": "$\\frac{2}{3}{{\\left( 2x+3 \\right)}^{\\frac{3}{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${{\\left( \\sqrt{2x+3} \\right)}^{\\prime }}=\\frac{1}{2\\sqrt{2x+3}}{{\\left( 2x+3 \\right)}^{\\prime }}=\\frac{1}{\\sqrt{2x+3}}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91483",
					"paperId": "1816662617877135360",
					"questionId": "57625",
					"questionName": "曲线$y=\\frac{4x-1}{{{(x-1)}^{2}}}$ （   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D70223E065FCFCFE0281A1",
							"examQuestionId": "57625",
							"optionName": "只有水平渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325750223E065FCFCFE0281A1",
							"examQuestionId": "57625",
							"optionName": "只有垂直渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4130223E065FCFCFE0281A1",
							"examQuestionId": "57625",
							"optionName": "没有渐近线",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B10223E065FCFCFE0281A1",
							"examQuestionId": "57625",
							"optionName": "既有水平渐近线又有垂直渐近线",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{4x-1}{{{(x-1)}^{2}}}=0$，又$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{4x-1}{{{(x-1)}^{2}}}=+\\infty $，故选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91484",
					"paperId": "1816662617877135360",
					"questionId": "57717",
					"questionName": "函数 $f(x)=2{{x}^{3}}-6{{x}^{2}}-18x-7$的极大值是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6DE0223E065FCFCFE0281A1",
							"examQuestionId": "57717",
							"optionName": "$f(-1)=3$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493257C0223E065FCFCFE0281A1",
							"examQuestionId": "57717",
							"optionName": "$f(3)=-61$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A41A0223E065FCFCFE0281A1",
							"examQuestionId": "57717",
							"optionName": "$f(1)=-29$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B80223E065FCFCFE0281A1",
							"examQuestionId": "57717",
							"optionName": "$f(0)=-7$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=6{{x}^{2}}-12x-18=6(x+1)(x-3)$，驻点${{x}_{1}}=-1,{{x}_{2}}=3,$$f(x)$在$(-\\infty ,-1]$上单调增加,在$\\left[ -1,3 \\right]$上单调减少",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91485",
					"paperId": "1816662617877135360",
					"questionId": "57704",
					"questionName": "利用洛必达法则求极限$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x}-\\frac{1}{{{e}^{x}}-1})$时，以下做法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3F40223E065FCFCFE0281A1",
							"examQuestionId": "57704",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x}-\\frac{1}{{{e}^{x}}-1})$$=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-1-x}{x({{e}^{x}}-1)}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322920223E065FCFCFE0281A1",
							"examQuestionId": "57704",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x}-\\frac{1}{{{e}^{x}}-1})$$=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\left[ {{\\left( \\frac{1}{x} \\right)}^{\\prime }}-{{\\left( \\frac{1}{{{e}^{x}}-1} \\right)}^{\\prime }} \\right]$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1300223E065FCFCFE0281A1",
							"examQuestionId": "57704",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x}-\\frac{1}{{{e}^{x}}-1})$$=\\infty -\\infty =0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961FCE0223E065FCFCFE0281A1",
							"examQuestionId": "57704",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x}-\\frac{1}{{{e}^{x}}-1})$$=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-1-x}{x({{e}^{x}}-1)}$$=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\left[ \\frac{{{e}^{x}}-1-x}{x({{e}^{x}}-1)} \\right]}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "对于$\\infty -\\infty $的未定式，第一步应该先将函数化简，满足$\\frac{0}{0}$或$\\frac{\\infty }{\\infty }$才能利用洛必达法则",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91486",
					"paperId": "1816662617877135360",
					"questionId": "57723",
					"questionName": "函数$f(x)=1-{{(x-2)}^{\\frac{2}{3}}}$的驻点是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4370223E065FCFCFE0281A1",
							"examQuestionId": "57723",
							"optionName": "$x=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322D50223E065FCFCFE0281A1",
							"examQuestionId": "57723",
							"optionName": "$x=-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1730223E065FCFCFE0281A1",
							"examQuestionId": "57723",
							"optionName": "$x=2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620110223E065FCFCFE0281A1",
							"examQuestionId": "57723",
							"optionName": "无驻点",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=-\\frac{2}{3}\\frac{1}{\\sqrt[3]{x-2}},{f}'(x)\\ne 0$，所以无驻点",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91487",
					"paperId": "1816662617877135360",
					"questionId": "57646",
					"questionName": "$\\underset{t\\to -2}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{t}}+1}{t}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4980223E065FCFCFE0281A1",
							"examQuestionId": "57646",
							"optionName": "$\\frac{1+{{e}^{2}}}{2{{e}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323360223E065FCFCFE0281A1",
							"examQuestionId": "57646",
							"optionName": "$-\\frac{{{e}^{2}}-1}{2{{e}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1D40223E065FCFCFE0281A1",
							"examQuestionId": "57646",
							"optionName": "$-\\frac{1+{{e}^{2}}}{2{{e}^{2}}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620720223E065FCFCFE0281A1",
							"examQuestionId": "57646",
							"optionName": "1",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{t\\to -2}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{t}}+1}{t}=\\frac{{{e}^{-2}}+1}{-2}=-\\frac{{{e}^{2}}+1}{2{{e}^{2}}}$，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91488",
					"paperId": "1816662617877135360",
					"questionId": "57604",
					"questionName": "下列各对函数相同的是（    ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A68C0223E065FCFCFE0281A1",
							"examQuestionId": "57604",
							"optionName": "$f(x)=x,g(x)={{(\\sqrt{x})}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493252A0223E065FCFCFE0281A1",
							"examQuestionId": "57604",
							"optionName": "$f(x)=\\sqrt{{{x}^{2}}},g(x)=|x|$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3C80223E065FCFCFE0281A1",
							"examQuestionId": "57604",
							"optionName": "$f(x)=x+1,g(x)=\\frac{{{x}^{2}}-1}{x-1}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622660223E065FCFCFE0281A1",
							"examQuestionId": "57604",
							"optionName": "$f(x)=\\lg {{x}^{2}},g(x)=2\\lg x$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "函数的两要素:定义域、对应关系.选项B中定义域、对应关系均相同.故选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91489",
					"paperId": "1816662617877135360",
					"questionId": "57741",
					"questionName": "曲线y = $\\frac{x-1}{3-x}$的垂直渐近线是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5560223E065FCFCFE0281A1",
							"examQuestionId": "57741",
							"optionName": "$x=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323F40223E065FCFCFE0281A1",
							"examQuestionId": "57741",
							"optionName": "$x=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2920223E065FCFCFE0281A1",
							"examQuestionId": "57741",
							"optionName": "$x=3$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621300223E065FCFCFE0281A1",
							"examQuestionId": "57741",
							"optionName": "无垂直渐近线",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由$\\underset{x\\to 3}{\\mathop{\\text{lim}}}\\,\\frac{x-1}{3-x}=\\infty $，可知",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91490",
					"paperId": "1816662617877135360",
					"questionId": "57602",
					"questionName": "设集合$P=\\left\\{ a,5,6,8 \\right\\}$,$M=\\left\\{ b,2,4,7 \\right\\}$.若$P\\bigcap M=\\left\\{ 4,5 \\right\\}$,则$a$,$b$取值为   （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5C70223E065FCFCFE0281A1",
							"examQuestionId": "57602",
							"optionName": "$a=4,b=5$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324650223E065FCFCFE0281A1",
							"examQuestionId": "57602",
							"optionName": "$a=4,b=6$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3030223E065FCFCFE0281A1",
							"examQuestionId": "57602",
							"optionName": "$a=2,b=5$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621A10223E065FCFCFE0281A1",
							"examQuestionId": "57602",
							"optionName": "$a=2,b=6$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "将$a$,$b$的代入，易知，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91491",
					"paperId": "1816662617877135360",
					"questionId": "57722",
					"questionName": "函数$f(x)=x-\\ln x$的极小值是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4360223E065FCFCFE0281A1",
							"examQuestionId": "57722",
							"optionName": "$f(-1)=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322D40223E065FCFCFE0281A1",
							"examQuestionId": "57722",
							"optionName": "$f(0)=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1720223E065FCFCFE0281A1",
							"examQuestionId": "57722",
							"optionName": "$f(2)=2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620100223E065FCFCFE0281A1",
							"examQuestionId": "57722",
							"optionName": "$f(1)=1$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=1-\\frac{1}{x}=\\frac{x-1}{x}$，得驻点$x=1$，在$\\left( 0,1 \\right)$上,${f}'(x)<0$:在$\\left( 1,+\\infty  \\right)$上,${f}'(x)>0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91492",
					"paperId": "1816662617877135360",
					"questionId": "57619",
					"questionName": "“函数$f\\left( x \\right)$在$x={{x}_{0}}$处有定义”是“$\\underset{x\\to {{x}_{0}}}{\\mathop{\\text{lim}}}\\,f(x)$存在”的 （   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5CD0223E065FCFCFE0281A1",
							"examQuestionId": "57619",
							"optionName": "必要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493246B0223E065FCFCFE0281A1",
							"examQuestionId": "57619",
							"optionName": "充分条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3090223E065FCFCFE0281A1",
							"examQuestionId": "57619",
							"optionName": "充要条件",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621A70223E065FCFCFE0281A1",
							"examQuestionId": "57619",
							"optionName": "无关条件",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由$x\\to {{x}_{0}}$时函数极限的定义知，选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91493",
					"paperId": "1816662617877135360",
					"questionId": "57611",
					"questionName": "函数$y=f\\left( x \\right)$与其反函数$y={{f}^{-1}}\\left( x \\right)$的图像关于   （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D40223E065FCFCFE0281A1",
							"examQuestionId": "57611",
							"optionName": "原点对称",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325720223E065FCFCFE0281A1",
							"examQuestionId": "57611",
							"optionName": "x轴对称",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4100223E065FCFCFE0281A1",
							"examQuestionId": "57611",
							"optionName": "y轴对称",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622AE0223E065FCFCFE0281A1",
							"examQuestionId": "57611",
							"optionName": "直线$y=x$对称",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由反函数的性质知，应选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91494",
					"paperId": "1816662617877135360",
					"questionId": "57703",
					"questionName": "利用洛必达法则求极限$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}+{{e}^{-x}}-2}{1-\\cos x}$时，以下做法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6DC0223E065FCFCFE0281A1",
							"examQuestionId": "57703",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}+{{e}^{-x}}-2}{1-\\cos x}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\ \\ \\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\left( \\frac{{{e}^{x}}+{{e}^{-x}}-2}{1-\\cos x} \\right)}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493257A0223E065FCFCFE0281A1",
							"examQuestionId": "57703",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}+{{e}^{-x}}-2}{1-\\cos x}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\ \\ \\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( {{e}^{x}}+{{e}^{-x}}-2 \\right)}^{\\prime }}}{1-\\cos x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4180223E065FCFCFE0281A1",
							"examQuestionId": "57703",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}+{{e}^{-x}}-2}{1-\\cos x}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\ \\ \\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}+{{e}^{-x}}-2}{{{\\left( 1-\\cos x \\right)}^{\\prime }}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B60223E065FCFCFE0281A1",
							"examQuestionId": "57703",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}+{{e}^{-x}}-2}{1-\\cos x}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\ \\ \\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( {{e}^{x}}+{{e}^{-x}}-2 \\right)}^{\\prime }}}{{{\\left( 1-\\cos x \\right)}^{\\prime }}}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "洛必达法则求极限的第一步是分子分母分别求导",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91495",
					"paperId": "1816662617877135360",
					"questionId": "57707",
					"questionName": "以下步骤中正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3F70223E065FCFCFE0281A1",
							"examQuestionId": "57707",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x-\\sin x}{{{x}^{3}}}$$\\overset{\\frac{0}{0}}{\\mathop{=}}\\,\\ \\ \\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,{{\\left( \\frac{x-\\sin x}{{{x}^{3}}} \\right)}^{\\prime }}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322950223E065FCFCFE0281A1",
							"examQuestionId": "57707",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( x-\\sin x \\right)}^{\\prime }}}{{{\\left( {{x}^{3}} \\right)}^{\\prime }}}$$=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{1+\\cos x}{3{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1330223E065FCFCFE0281A1",
							"examQuestionId": "57707",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{1-\\cos x}{3{{x}^{2}}}\\overset{\\frac{0}{0}}{\\mathop{=}}\\,$$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( 1-\\cos x \\right)}^{\\prime }}}{{{\\left( 3{{x}^{2}} \\right)}^{\\prime }}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961FD10223E065FCFCFE0281A1",
							"examQuestionId": "57707",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{\\left( 1-\\cos x \\right)}^{\\prime }}}{{{\\left( 3{{x}^{2}} \\right)}^{\\prime }}}$$=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{-\\sin x}{6{{x}^{{}}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "考察洛必达法则使用的前提、方法、步骤",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91496",
					"paperId": "1816662617877135360",
					"questionId": "57601",
					"questionName": "下列集合中空集是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A59B0223E065FCFCFE0281A1",
							"examQuestionId": "57601",
							"optionName": "$\\left\\{ 1,2,3 \\right\\}\\bigcap \\left\\{ 3,5,6 \\right\\}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324390223E065FCFCFE0281A1",
							"examQuestionId": "57601",
							"optionName": "$\\left\\{ 0,1,2 \\right\\}\\bigcap \\left\\{ 3,5,6 \\right\\}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2D70223E065FCFCFE0281A1",
							"examQuestionId": "57601",
							"optionName": "$\\left\\{ \\left( x,y \\right)|y={{x}^{2}} \\right\\}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621750223E065FCFCFE0281A1",
							"examQuestionId": "57601",
							"optionName": "$\\left\\{ x\\left| |x-1|&lt;\\frac{1}{2} \\right. \\right\\}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由交集及空集的概念知，应选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91497",
					"paperId": "1816662617877135360",
					"questionId": "57617",
					"questionName": "若数列$\\{{{x}_{n}}\\}$与数列$\\{{{y}_{n}}\\}$的极限分别为$a$与$b$,且$a\\ne b$,则数列${{x}_{1}},{{y}_{1}},{{x}_{2}},{{y}_{2}},{{x}_{3}},{{y}_{3}},...$的极限为 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5CC0223E065FCFCFE0281A1",
							"examQuestionId": "57617",
							"optionName": "$a$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493246A0223E065FCFCFE0281A1",
							"examQuestionId": "57617",
							"optionName": "$b$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3080223E065FCFCFE0281A1",
							"examQuestionId": "57617",
							"optionName": "$a$ + $b$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621A60223E065FCFCFE0281A1",
							"examQuestionId": "57617",
							"optionName": "不存在",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由数列极限的定义知，选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91498",
					"paperId": "1816662617877135360",
					"questionId": "57686",
					"questionName": "若$f(x)={{\\left( 1-2x \\right)}^{9}}$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7380223E065FCFCFE0281A1",
							"examQuestionId": "57686",
							"optionName": "$9{{\\left( 1-2x \\right)}^{8}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D60223E065FCFCFE0281A1",
							"examQuestionId": "57686",
							"optionName": "$18{{\\left( 1-2x \\right)}^{8}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4740223E065FCFCFE0281A1",
							"examQuestionId": "57686",
							"optionName": "$-9{{\\left( 1-2x \\right)}^{8}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623120223E065FCFCFE0281A1",
							"examQuestionId": "57686",
							"optionName": "$-18{{\\left( 1-2x \\right)}^{8}}$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=9{{\\left( 1-2x \\right)}^{8}}{{\\left( 1-2x \\right)}^{\\prime }}=-18{{\\left( 1-2x \\right)}^{8}}$ ，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91499",
					"paperId": "1816662617877135360",
					"questionId": "57729",
					"questionName": "关于曲线$y={{x}^{2}}$，下列说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4740223E065FCFCFE0281A1",
							"examQuestionId": "57729",
							"optionName": "在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$ 上单调增加",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549323120223E065FCFCFE0281A1",
							"examQuestionId": "57729",
							"optionName": "在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$ 上单调减少",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1B00223E065FCFCFE0281A1",
							"examQuestionId": "57729",
							"optionName": "$\\left( \\ 0\\ ,\\ 0\\  \\right)$是该曲线拐点",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496204E0223E065FCFCFE0281A1",
							"examQuestionId": "57729",
							"optionName": "$x=0$是它的极小点",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'={{\\left( {{x}^{2}} \\right)}^{\\prime }}=2x$，$x<0$时，${y}'<0$曲线单调减少，$x>0$时，${y}'>0$，单调曲线增加",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91500",
					"paperId": "1816662617877135360",
					"questionId": "57626",
					"questionName": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x-1}-\\frac{2}{{{x}^{2}}-1})$=（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5CE0223E065FCFCFE0281A1",
							"examQuestionId": "57626",
							"optionName": "$-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493246C0223E065FCFCFE0281A1",
							"examQuestionId": "57626",
							"optionName": "$\\frac{1}{2}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A30A0223E065FCFCFE0281A1",
							"examQuestionId": "57626",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621A80223E065FCFCFE0281A1",
							"examQuestionId": "57626",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,(\\frac{1}{x-1}-\\frac{2}{{{x}^{2}}-1})=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{x+1-2}{(x-1)(x+1)}=\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{1}{x+1}=\\frac{1}{2}$.故选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91501",
					"paperId": "1816662617877135360",
					"questionId": "57711",
					"questionName": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{x-1}{3{{x}^{2}}-2x-1}=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A43C0223E065FCFCFE0281A1",
							"examQuestionId": "57711",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322DA0223E065FCFCFE0281A1",
							"examQuestionId": "57711",
							"optionName": "1",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1780223E065FCFCFE0281A1",
							"examQuestionId": "57711",
							"optionName": "$\\frac{1}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620160223E065FCFCFE0281A1",
							"examQuestionId": "57711",
							"optionName": "1/4",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 1}{\\mathop{\\text{lim}}}\\,\\frac{x-1}{3{{x}^{2}}-2x-1}=\\frac{1}{4}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91502",
					"paperId": "1816662617877135360",
					"questionId": "57731",
					"questionName": "关于曲线$y=\\ln x$，下列说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A62D0223E065FCFCFE0281A1",
							"examQuestionId": "57731",
							"optionName": "在$\\left( \\ 0\\ ,\\ +\\infty \\  \\right)$ 上是凸的",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324CB0223E065FCFCFE0281A1",
							"examQuestionId": "57731",
							"optionName": "在$\\left( \\ 0\\ ,\\ +\\infty \\  \\right)$ 上凹的",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3690223E065FCFCFE0281A1",
							"examQuestionId": "57731",
							"optionName": "在$\\left( \\ 0\\ ,\\ +\\infty \\  \\right)$ 上有拐点",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622070223E065FCFCFE0281A1",
							"examQuestionId": "57731",
							"optionName": "在$\\left( \\ 0\\ ,\\ +\\infty \\  \\right)$上单调递减",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "定义域为$\\left( \\ 0\\ ,\\ +\\infty \\  \\right)$，在定义域内是单调增加，${y}''<0$，在定义域内是凸的",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91503",
					"paperId": "1816662617877135360",
					"questionId": "57660",
					"questionName": "曲线$y=2{{x}^{2}}$在$x=1$处的切线方程为（）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A60B0223E065FCFCFE0281A1",
							"examQuestionId": "57660",
							"optionName": "$y=4x-1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324A90223E065FCFCFE0281A1",
							"examQuestionId": "57660",
							"optionName": "$y=4x-2$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3470223E065FCFCFE0281A1",
							"examQuestionId": "57660",
							"optionName": "$y=4x-3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621E50223E065FCFCFE0281A1",
							"examQuestionId": "57660",
							"optionName": "$y=4x-4$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$k=4x{{|}_{x=1}}=4$，切线为$y-2=4\\left( x-1 \\right)$， 即$y=4x-2$ ， 选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91504",
					"paperId": "1816662617877135360",
					"questionId": "57609",
					"questionName": "下列函数中是隐函数的为（其中$x>0$） （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5C80223E065FCFCFE0281A1",
							"examQuestionId": "57609",
							"optionName": "$y=\\arcsin x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324660223E065FCFCFE0281A1",
							"examQuestionId": "57609",
							"optionName": "$y=\\sin \\left( x\\text{ }+\\text{ }y \\right)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3040223E065FCFCFE0281A1",
							"examQuestionId": "57609",
							"optionName": "$y=1+x\\cdot {{2}^{x}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621A20223E065FCFCFE0281A1",
							"examQuestionId": "57609",
							"optionName": "$y={{x}^{\\sin x}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由隐函数定义知，应选B.",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91505",
					"paperId": "1816662617877135360",
					"questionId": "57678",
					"questionName": "若$f(x)$=$\\arctan \\frac{1}{x}$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6A30223E065FCFCFE0281A1",
							"examQuestionId": "57678",
							"optionName": "$\\frac{1}{1+x{}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325410223E065FCFCFE0281A1",
							"examQuestionId": "57678",
							"optionName": "$-\\frac{1}{1+x{}^{2}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3DF0223E065FCFCFE0281A1",
							"examQuestionId": "57678",
							"optionName": "$\\frac{{{x}^{2}}}{1+x{}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496227D0223E065FCFCFE0281A1",
							"examQuestionId": "57678",
							"optionName": "$-\\frac{{{x}^{2}}}{1+x{}^{2}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=\\frac{1}{1+{{(\\frac{1}{x})}^{2}}}\\cdot (\\frac{1}{x}{)}'=-\\frac{1}{1+{{x}^{2}}}$ ，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91506",
					"paperId": "1816662617877135360",
					"questionId": "57692",
					"questionName": "若$f(x)=\\cos \\text{ }x$,则${f}''(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6D90223E065FCFCFE0281A1",
							"examQuestionId": "57692",
							"optionName": "$~\\sin \\text{ }x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325770223E065FCFCFE0281A1",
							"examQuestionId": "57692",
							"optionName": "$-\\sin \\text{ }x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4150223E065FCFCFE0281A1",
							"examQuestionId": "57692",
							"optionName": "$\\cos \\text{ }x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622B30223E065FCFCFE0281A1",
							"examQuestionId": "57692",
							"optionName": "$-\\cos \\text{ }x$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=-\\sin \\text{ }x$ ，${f}''(x)=-\\cos \\text{ }x$ 选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91507",
					"paperId": "1816662617877135360",
					"questionId": "57738",
					"questionName": "曲线y =${{x}^{3}}$的凹区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4390223E065FCFCFE0281A1",
							"examQuestionId": "57738",
							"optionName": "$(0,+\\infty )$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322D70223E065FCFCFE0281A1",
							"examQuestionId": "57738",
							"optionName": "$(-\\infty ,0)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1750223E065FCFCFE0281A1",
							"examQuestionId": "57738",
							"optionName": "$(-\\infty ,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620130223E065FCFCFE0281A1",
							"examQuestionId": "57738",
							"optionName": "$(-1,1)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'=3{{x}^{2}},{y}''=6x,{y}''=0\\text{ } x=0$，当$x>0$时,${y}''>0$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91508",
					"paperId": "1816662617877135360",
					"questionId": "57624",
					"questionName": "如果$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,f(x)=\\infty ,\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\text{g}(x)=\\infty $，下列极限成立的是 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6CE0223E065FCFCFE0281A1",
							"examQuestionId": "57624",
							"optionName": "$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,[f(x)+g(x)]=\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493256C0223E065FCFCFE0281A1",
							"examQuestionId": "57624",
							"optionName": "$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,[f(x)-g(x)]=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A40A0223E065FCFCFE0281A1",
							"examQuestionId": "57624",
							"optionName": "$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{1}{f(x)+g(x)}=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622A80223E065FCFCFE0281A1",
							"examQuestionId": "57624",
							"optionName": "$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{1}{f(x)}=0$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由无穷小与无穷大的关系知，选D。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91509",
					"paperId": "1816662617877135360",
					"questionId": "57676",
					"questionName": "若$f(x)=\\sin \\left( {{x}^{2}} \\right)$,则${f}'(x)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6A20223E065FCFCFE0281A1",
							"examQuestionId": "57676",
							"optionName": "$\\cos \\left( {{x}^{2}} \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325400223E065FCFCFE0281A1",
							"examQuestionId": "57676",
							"optionName": "$2\\cos \\left( {{x}^{2}} \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3DE0223E065FCFCFE0281A1",
							"examQuestionId": "57676",
							"optionName": "$2x\\cos \\left( {{x}^{2}} \\right)$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496227C0223E065FCFCFE0281A1",
							"examQuestionId": "57676",
							"optionName": "$x\\cos \\left( {{x}^{2}} \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)=\\cos ({{x}^{2}})({{x}^{2}}{)}'=2x\\cos ({{x}^{2}})$ ，选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91510",
					"paperId": "1816662617877135360",
					"questionId": "57645",
					"questionName": "函数$f\\left( x \\right)=\\left\\{ \\begin{matrix}   2x,\\quad \\quad 0\\le x<1  \\\\   a-3x,\\ \\ 1\\le x<2  \\\\\\end{matrix} \\right.$,在点$x=1$处连续，则$a=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7020223E065FCFCFE0281A1",
							"examQuestionId": "57645",
							"optionName": "$2$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325A00223E065FCFCFE0281A1",
							"examQuestionId": "57645",
							"optionName": "$5$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A43E0223E065FCFCFE0281A1",
							"examQuestionId": "57645",
							"optionName": "$3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622DC0223E065FCFCFE0281A1",
							"examQuestionId": "57645",
							"optionName": "$4$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由函数f(x)在x=1处连续的条件知，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91511",
					"paperId": "1816662617877135360",
					"questionId": "57674",
					"questionName": "若$f(x)={{x}^{3}}-2x+1$,则${f}'(1)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A3C00223E065FCFCFE0281A1",
							"examQuestionId": "57674",
							"optionName": "1",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493225E0223E065FCFCFE0281A1",
							"examQuestionId": "57674",
							"optionName": "2",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A0FC0223E065FCFCFE0281A1",
							"examQuestionId": "57674",
							"optionName": "3",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "103654961F9A0223E065FCFCFE0281A1",
							"examQuestionId": "57674",
							"optionName": "4",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(1)=\\left( 3{{x}^{2}}-2 \\right){{|}_{x=1}}=1$  ，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91512",
					"paperId": "1816662617877135360",
					"questionId": "57684",
					"questionName": "已知$f\\left( x \\right)=\\cos 3x$，则${f}'\\left( x \\right)=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7370223E065FCFCFE0281A1",
							"examQuestionId": "57684",
							"optionName": "$3\\sin x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D50223E065FCFCFE0281A1",
							"examQuestionId": "57684",
							"optionName": "$\\sin 3x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4730223E065FCFCFE0281A1",
							"examQuestionId": "57684",
							"optionName": "$-\\sin 3x$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623110223E065FCFCFE0281A1",
							"examQuestionId": "57684",
							"optionName": "$-3\\sin 3x$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "${{\\left( \\cos 3x \\right)}^{\\prime }}=-\\sin 3x{{\\left( 3x \\right)}^{\\prime }}=-3\\sin 3x$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91513",
					"paperId": "1816662617877135360",
					"questionId": "57631",
					"questionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sin 3x}{\\sin 5x}=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A45E0223E065FCFCFE0281A1",
							"examQuestionId": "57631",
							"optionName": "$\\frac{5}{3}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322FC0223E065FCFCFE0281A1",
							"examQuestionId": "57631",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A19A0223E065FCFCFE0281A1",
							"examQuestionId": "57631",
							"optionName": "$\\frac{3}{5}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620380223E065FCFCFE0281A1",
							"examQuestionId": "57631",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sin 3x}{\\sin 5x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{3x}{5x}=\\frac{3}{5}$，故选C",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91514",
					"paperId": "1816662617877135360",
					"questionId": "57685",
					"questionName": "已知$y=\\arcsin \\left( -x \\right)$，则$\\frac{dy}{dx}=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6A40223E065FCFCFE0281A1",
							"examQuestionId": "57685",
							"optionName": "$\\frac{1}{\\sqrt{1-{{x}^{2}}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325420223E065FCFCFE0281A1",
							"examQuestionId": "57685",
							"optionName": "$-\\frac{1}{\\sqrt{1-{{x}^{2}}}}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3E00223E065FCFCFE0281A1",
							"examQuestionId": "57685",
							"optionName": "$\\frac{1}{1+{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365496227E0223E065FCFCFE0281A1",
							"examQuestionId": "57685",
							"optionName": "$-\\frac{1}{1+{{x}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${{\\left[ \\arcsin \\left( -x \\right) \\right]}^{\\prime }}=\\frac{1}{\\sqrt{1-{{x}^{2}}}}{{\\left( -x \\right)}^{\\prime }}=-\\frac{1}{\\sqrt{1-{{x}^{2}}}}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91515",
					"paperId": "1816662617877135360",
					"questionId": "57695",
					"questionName": "若$y={{e}^{x}}$,则$d\\text{ }y{{|}_{x=1}}=$ （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A73A0223E065FCFCFE0281A1",
							"examQuestionId": "57695",
							"optionName": "$e$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D80223E065FCFCFE0281A1",
							"examQuestionId": "57695",
							"optionName": "$edx$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4760223E065FCFCFE0281A1",
							"examQuestionId": "57695",
							"optionName": "$2e$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623140223E065FCFCFE0281A1",
							"examQuestionId": "57695",
							"optionName": "$2edx$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${y}'={{e}^{x}}$ ，   $dy{{\\left| _{x=1}={{e}^{x}}dx \\right|}_{x=1}}=edx$ ，选B",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91516",
					"paperId": "1816662617877135360",
					"questionId": "57616",
					"questionName": "设$f\\left( x \\right)$是奇函数，且$\\varphi \\left( x \\right)=f(x)\\cdot \\sin x+1$，则$\\varphi \\left( x \\right)$奇偶性是 （  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A45B0223E065FCFCFE0281A1",
							"examQuestionId": "57616",
							"optionName": "偶函数",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322F90223E065FCFCFE0281A1",
							"examQuestionId": "57616",
							"optionName": "奇函数",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1970223E065FCFCFE0281A1",
							"examQuestionId": "57616",
							"optionName": "非奇非偶函数",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620350223E065FCFCFE0281A1",
							"examQuestionId": "57616",
							"optionName": "不能确定",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "由奇、偶函数的定义即相关运算知，选A。",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91517",
					"paperId": "1816662617877135360",
					"questionId": "57627",
					"questionName": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{4{{n}^{3}}-n+1}{5{{n}^{3}}+{{n}^{2}}+n}=$（   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A6FE0223E065FCFCFE0281A1",
							"examQuestionId": "57627",
							"optionName": "$\\frac{4}{5}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493259C0223E065FCFCFE0281A1",
							"examQuestionId": "57627",
							"optionName": "$0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A43A0223E065FCFCFE0281A1",
							"examQuestionId": "57627",
							"optionName": "$\\frac{1}{2}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549622D80223E065FCFCFE0281A1",
							"examQuestionId": "57627",
							"optionName": "$\\infty $",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\underset{n\\to \\infty }{\\mathop{\\text{lim}}}\\,\\frac{4{{n}^{3}}-n+1}{5{{n}^{3}}+{{n}^{2}}+n}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{4-\\frac{1}{{{n}^{2}}}+\\frac{1}{{{n}^{3}}}}{5+\\frac{1}{n}+\\frac{1}{{{n}^{2}}}}=\\frac{4}{5}$.故选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91518",
					"paperId": "1816662617877135360",
					"questionId": "57693",
					"questionName": "若$f(x)={{e}^{x}}+{{x}^{3}}$,则${f}''(1)$= （）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A7390223E065FCFCFE0281A1",
							"examQuestionId": "57693",
							"optionName": "$e\\text{ }+\\text{ }6$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549325D70223E065FCFCFE0281A1",
							"examQuestionId": "57693",
							"optionName": "$e\\text{ }-\\text{ }6$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A4750223E065FCFCFE0281A1",
							"examQuestionId": "57693",
							"optionName": "$e\\text{ }+\\text{ }3$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549623130223E065FCFCFE0281A1",
							"examQuestionId": "57693",
							"optionName": "$e\\text{ }-\\text{ }3$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}'(x)={{e}^{x}}+3{{x}^{2}}$ ， ${f}''(x)={{e}^{x}}+6x$ ， ${f}''(1)={{e}^{1}}+6=e+6$ ，选A",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91519",
					"paperId": "1816662617877135360",
					"questionId": "57730",
					"questionName": "设$y=\\sin x$，下列说法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5F90223E065FCFCFE0281A1",
							"examQuestionId": "57730",
							"optionName": "函数$y=\\sin x$在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$上有最大值1",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549324970223E065FCFCFE0281A1",
							"examQuestionId": "57730",
							"optionName": "曲线$y=\\sin x$在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$上没有拐点",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A3350223E065FCFCFE0281A1",
							"examQuestionId": "57730",
							"optionName": "曲线$y=\\sin x$在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$ 上单调增加",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621D30223E065FCFCFE0281A1",
							"examQuestionId": "57730",
							"optionName": "曲线$y=\\sin x$在$\\left( \\ -\\infty \\ ,\\ +\\infty \\  \\right)$ 上单调减少",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "通过正弦函数图象可以得出",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91520",
					"paperId": "1816662617877135360",
					"questionId": "57603",
					"questionName": "设$A=\\left\\{ x\\left| x>3 \\right. \\right\\}$ ,$B=\\left\\{ x|x>5 \\right\\}$,则$A\\cup B$=  （   ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A59C0223E065FCFCFE0281A1",
							"examQuestionId": "57603",
							"optionName": "$\\left( 3,5 \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493243A0223E065FCFCFE0281A1",
							"examQuestionId": "57603",
							"optionName": "$\\left( 5,+\\infty  \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2D80223E065FCFCFE0281A1",
							"examQuestionId": "57603",
							"optionName": "$[3,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621760223E065FCFCFE0281A1",
							"examQuestionId": "57603",
							"optionName": "$(3,+\\infty )$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "由并集的运算的定义知,选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91521",
					"paperId": "1816662617877135360",
					"questionId": "57613",
					"questionName": "设$f\\left( x \\right)=lgx$,则$f\\left( x \\right)+f\\left( y \\right)=$（  ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A4580223E065FCFCFE0281A1",
							"examQuestionId": "57613",
							"optionName": "$f\\left( \\frac{y}{x} \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322F60223E065FCFCFE0281A1",
							"examQuestionId": "57613",
							"optionName": "$f\\left( x+y \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1940223E065FCFCFE0281A1",
							"examQuestionId": "57613",
							"optionName": "$f\\left( \\frac{x}{y} \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620320223E065FCFCFE0281A1",
							"examQuestionId": "57613",
							"optionName": "$f(xy)$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "$f\\left( x \\right)+f\\left( y \\right)=\\lg x+\\lg y=\\lg xy$. 故选D",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91522",
					"paperId": "1816662617877135360",
					"questionId": "57682",
					"questionName": "已知$f\\left( x \\right)=\\ln \\left( 1-2x \\right)$，则${f}'\\left( x \\right)=$（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A5BF0223E065FCFCFE0281A1",
							"examQuestionId": "57682",
							"optionName": "$\\frac{-2}{1-2x}$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365493245D0223E065FCFCFE0281A1",
							"examQuestionId": "57682",
							"optionName": "$\\frac{1}{1-2x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A2FB0223E065FCFCFE0281A1",
							"examQuestionId": "57682",
							"optionName": "$\\frac{2}{1-2x}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549621990223E065FCFCFE0281A1",
							"examQuestionId": "57682",
							"optionName": "$\\ln \\left( 1-2x \\right)$",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "$\\left[ \\ln \\left( 1-2x \\right) \\right]{{\\ }^{\\prime }}=\\frac{1}{1-2x}{{\\left( 1-2x \\right)}^{\\prime }}=\\frac{-2}{1-x}$",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91523",
					"paperId": "1816662617877135360",
					"questionId": "57709",
					"questionName": "下列解法正确的是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A43B0223E065FCFCFE0281A1",
							"examQuestionId": "57709",
							"optionName": "$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{{{x}^{4}}-{{a}^{4}}}{{{x}^{3}}-{{a}^{3}}}=\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{4{{x}^{3}}-4{{a}^{3}}}{3{{x}^{3}}-3{{a}^{2}}}$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322D90223E065FCFCFE0281A1",
							"examQuestionId": "57709",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{{{e}^{x}}-x-1}{x({{e}^{x}}-1)}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{x-x}{x\\cdot x}=0$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A1770223E065FCFCFE0281A1",
							"examQuestionId": "57709",
							"optionName": "$\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\sin 3x}{\\sin 5x}=\\underset{x\\to 0}{\\mathop{\\text{lim}}}\\,\\frac{\\cos 3x}{\\cos 5x}=1$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620150223E065FCFCFE0281A1",
							"examQuestionId": "57709",
							"optionName": "$\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{{{x}^{4}}-{{a}^{4}}}{{{x}^{3}}-{{a}^{3}}}=\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{4{{x}^{3}}}{3{{x}^{2}}}=\\underset{x\\to a}{\\mathop{\\text{lim}}}\\,\\frac{4}{3}{{x}^{3-2}}=\\frac{4}{3}a$",
							"isTrue": "1",
							"isChoose": "0"
						}
					],
					"explanation": "A中应该把a看成常数，B中最后一步错误，C中第一步错误",
					"answerVersionId": "1823895035833643008"
				},
				{
					"paperDetailId": "91524",
					"paperId": "1816662617877135360",
					"questionId": "57725",
					"questionName": "函数$f(x)=1-{{(x-2)}^{\\frac{2}{3}}}$的单调增区间是（ ）",
					"questionScore": "1",
					"questionOptionList": [{
							"examQuestionOptionId": "10365491A43F0223E065FCFCFE0281A1",
							"examQuestionId": "57725",
							"optionName": "$[2,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549322DD0223E065FCFCFE0281A1",
							"examQuestionId": "57725",
							"optionName": "$(-\\infty ,+\\infty )$",
							"isTrue": "0",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "10365494A17B0223E065FCFCFE0281A1",
							"examQuestionId": "57725",
							"optionName": "$(-\\infty ,2]$",
							"isTrue": "1",
							"isChoose": "0"
						},
						{
							"examQuestionOptionId": "1036549620190223E065FCFCFE0281A1",
							"examQuestionId": "57725",
							"optionName": "不存在",
							"isTrue": "0",
							"isChoose": "0"
						}
					],
					"explanation": "${f}&#39;(x)=-\\frac{2}{3}\\frac{1}{\\sqrt[3]{x-2}}$，在$(-\\infty ,2)$上,${f}&#39;(x)&gt;0$，在$(-\\infty ,2]$上单调递增",
					"answerVersionId": "1823895035833643008"
				}
			],
			"answerVersionId": "1823895035833643008"
		}]
	}
	callback(res)
}
